RhizMicrobiome_GenusLevel
Sara Colom
2/8/2020
Sample sizes
Table sample number by species and treatment
| Species | Treatment | N |
|---|---|---|
| I. purpurea | Alone | 27 |
| I. purpurea | Competition | 78 |
| I. hederacea | Competition | 78 |
Table number of maternal line per species
| Species | Number of ML |
|---|---|
| I. purpurea | 10 |
| I. hederacea | 5 |
Load Libraries
library(phyloseq)
library(ggplot2)
library(ape)
library(vegan)
library(plyr)
library(dplyr)
library(scales)
library(grid)
library(reshape2)
library(DESeq2)
library(pegas)
library(pgirmess)
library(multcomp)
library(multcompView)
library(ggpubr)
library(ggcorrplot)
library(RColorBrewer)
library(plotly)
library(ggthemes)
library(corrplot)
library(Hmisc)
library(emmeans)
library(lmerTest)
source("~/Google Drive File Stream/My Drive/IDM_Experiments-master/miSeq.R")
# Aesthetics
Tx<-theme(axis.text.y = element_text(size=20),
axis.title.y = element_text(size=20))+
theme(axis.text.x = element_text(vjust = 1, hjust=1,angle=0,size=20),
axis.title.x = element_text(angle=0,size=20),
plot.title=element_text(size=25,hjust=0))
# Margins
Margin<-theme(
panel.background = element_rect(fill = "white"),
plot.margin = margin(2, 2, 2, 2, "cm"),
plot.background = element_rect(
fill = "white",
colour = "black",
size = 1
)
)
# Aesthetics
Tx2<-theme(axis.text.y = element_text(size=20),
axis.title.y = element_text(size=25))+
theme(axis.text.x = element_text(vjust = 1, hjust=1,size=25),
axis.title.x = element_text(size=25),
plot.title=element_text(size=25,hjust=0))
GoldGrey=c("#F1CE63","#79706E")
GreenBlue=c("#59A14F","#4E79A7")Sequence data analysis
### loading mothur output with FWDB+silva taxonomy and sample metadata.
### Experiments run in
# Read in mothur output (NOTE you can download mothur output data HERE: https://drive.google.com/drive/folders/1u_KjbdsIcwLEA_Yh4MCYrexvj0YWQrxb?usp=sharing)
setwd("/Volumes/GoogleDrive/My Drive/Baucom Lab /Chapter3MicrobiomeMothur/Subset_Mothur_Output/")
sharedfile <- "stability.trim.contigs.good.unique.good.filter.unique.precluster.pick.pick.opti_mcc.shared"
taxfile <- "stability.trim.contigs.good.unique.good.filter.unique.precluster.pick.pick.opti_mcc.0.03.cons.taxonomy"
mothurdata <- import_mothur(mothur_shared_file = sharedfile,mothur_constaxonomy_file = taxfile)
setwd("/Volumes/GoogleDrive/My Drive/Baucom Lab /Chapter3MicrobiomeMothur/Microbiome_2018/DataSets/MothurOutput_Mock_Microbiome/Microbiome_Output")
sampledata= read.csv('MetaDataTest.csv')
SAMPLE=sampledata
row.names(SAMPLE)=SAMPLE$Sample_ID
SAMPLE=subset(SAMPLE,SAMPLE$TRT=="Alone"|SAMPLE$TRT=="Inter")
SAMPLE=sample_data(SAMPLE)
### create phyloseq object
physeq.all = merge_phyloseq(mothurdata, SAMPLE) # Modified version worked
### We need to change the taxonomy names: when using the fwdb taxonomy we need to add different headers after removing the last column, which contains no information except for 1 Verrucomicrobia taxon
# tax_table(physeq.all) <- tax_table(physeq.all)[,-7] # this removes the final column
colnames(tax_table(physeq.all))<-c("Kingdom","Phylum","Class","Order","Family","Genus")
# tax_table(physeq.all) <-cbind(tax_table(physeq.all),row.names(tax_table(physeq.all)))
### removing non-bacterial reads (was already done in mothur, but just to be safe after merging taxonomies)
# physeq.all <- subset_taxa(physeq.all, Kingdom == "Bacteria")## Aggregate at the genus level, then saving ea componant externally to reload and save time.
# physeq_genus <- physeq.all %>%
#tax_glom(taxrank = "Genus")
# otu=data.frame(otu_table(physeq_genus))
# meta=data.frame(sample_data(physeq_genus))
# tax=data.frame(tax_table(physeq_genus))
# write.csv(x = otu,file = "otu_table.csv",row.names = TRUE)
# write.csv(x = tax,file = "tax_table.csv")#
# write.csv(x = meta,file = "sample_table.csv",row.names = F)
otu=read.csv("~/Google Drive File Stream/My Drive/Baucom Lab /Chapter3MicrobiomeMothur/Microbiome_2018/DataSets/MothurOutput_Mock_Microbiome/Microbiome_Output/otu_table.csv",row.names = 1)
colnames(otu)=gsub('X',"",colnames(otu))
otu=otu_table(otu,taxa_are_rows = TRUE)
tax=read.csv('~/Google Drive File Stream/My Drive/Baucom Lab /Chapter3MicrobiomeMothur/Microbiome_2018/DataSets/MothurOutput_Mock_Microbiome/Microbiome_Output/tax_table.csv',row.names=1)
taxRows=row.names(tax)
taxCols=colnames(tax)
tax=tax_table(as.matrix(tax))
#row.names(tax)=taxRows
#colnames(tax)=taxCols
meta=read.csv('~/Google Drive File Stream/My Drive/Baucom Lab /Chapter3MicrobiomeMothur/Microbiome_2018/DataSets/MothurOutput_Mock_Microbiome/Microbiome_Output/MetaDataTest.csv')
namesKeep<-colnames(otu)
row.names(meta)=meta$Sample_ID
meta=meta[which(meta$Sample_ID%in%namesKeep),]
meta=sample_data(meta)
physeq_genus=merge_phyloseq(otu,tax,meta)setwd("~/Google Drive File Stream/My Drive/Baucom Lab /Chapter3MicrobiomeMothur/Microbiome_2018/DataSets/MothurOutput_Mock_Microbiome/Microbiome_Output")
### ADD THE PROTEOBACTERIA CLASSES TO THE PHYLA NAME FIELD IN PHYLOSEQ OBJECT TAXONOMY
phy <- data.frame(tax_table(physeq_genus))
Phylum <- as.character(phy$Phylum)
Class <- as.character(phy$Class)
for (i in 1:length(Phylum)){
if (Phylum[i] == "Proteobacteria"){
if (Class[i] == "unclassified"){
Phylum[i] <- Phylum[i]
} else {
Phylum[i] <- Class[i]
}
}
}
Phylum<-as.character(phy$Phylum)
Class=as.character(phy$Class)
phy$Phylum=Phylum
t <- tax_table(as.matrix(phy))Sequence depth and pruning
physeq=(physeq.all2)
physeq <- prune_taxa(taxa_sums(physeq) > 0, physeq) # Remove taxa with no counts
#check number of reads in each sample, differences in count are in part due differet numbers of chlorophyl reads depending on time of experiment
# Make a data frame with a column for the read counts of each sample
sample_sum_df <- data.frame(sum = sample_sums(physeq))
# Histogram of sample read counts
ggplot(sample_sum_df, aes(x = sum)) +
geom_histogram(color = "black", fill = "#59A14F", binwidth = 2500) +
ggtitle("Distribution of sample sequencing depth") +
xlab("Read counts") +
theme(axis.title.y = element_blank())+
theme_classic()
# Scales reads to smallest library size
source("https://raw.githubusercontent.com/michberr/MicrobeMiseq/master/R/miseqR.R")
#physeq.scale <- scale_reads(physeq, min(sample_sums(physeq)))
##### Normalization #######
# Scales reads by
# 1) taking proportions,
# 2) multiplying by a given library size of n
# 3) rounding down
physeq1=prune_samples(sample_sums(physeq) >20000, physeq)
sample_sum_df1 <- data.frame(sum = sample_sums(physeq1))
# Histogram of sample read counts
ggplot(sample_sum_df1, aes(x = sum)) +
geom_histogram(color = "black", fill = "#59A14F", binwidth = 2500) +
ggtitle("Distribution of sample sequencing depth after pruning") +
xlab("Read counts") +
theme(axis.title.y = element_blank())+
theme_classic()
n=min(sample_sums(physeq1))
physeq.scale <-
transform_sample_counts(physeq1, function(x) {
(n * x/sum(x)) # Transform to rel. abundance
})
physeq.scale <- prune_taxa(taxa_sums(physeq.scale) > 0, physeq.scale)
physeq1## phyloseq-class experiment-level object
## otu_table() OTU Table: [ 1098 taxa and 173 samples ]
## sample_data() Sample Data: [ 173 samples by 9 sample variables ]
## tax_table() Taxonomy Table: [ 1098 taxa by 6 taxonomic ranks ]# Betadiv pcoa Bray-Curtis DNA only
physeq.pcoa <-
ordinate(
physeq = physeq.scale,
method = "PCoA",
distance = "bray"
)
physeq.pcoa.vectors <- data.frame(physeq.pcoa$vectors[, 1:4])
physeq.pcoa.vectors$Duplicates <- row.names(physeq.pcoa.vectors)
SampData=data.frame(sample_data(physeq))
colnames(SampData)[1]="Duplicates"
SampData=subset(SampData,SampData$TRT=="Inter"|SampData$TRT=="Alone")
physeq.pcoa.df <- droplevels(merge(physeq.pcoa.vectors,SampData,by="Duplicates"))
bray_values <- physeq.pcoa$values
bray_rel_eigens <- bray_values$Relative_eig
bray_rel_eigen1 <- bray_rel_eigens[1]
bray_rel_eigen1_percent <- round(bray_rel_eigen1 * 100, digits = 1)
bray_rel_eigen2 <- bray_rel_eigens[2]
bray_rel_eigen2_percent <- round(bray_rel_eigen2 * 100, digits = 1)
bray_rel_eigen3 <- bray_rel_eigens[3]
bray_rel_eigen3_percent <- round(bray_rel_eigen3 * 100, digits = 1)
bray_rel_eigen4 <- bray_rel_eigens[4]
bray_rel_eigen4_percent <- round(bray_rel_eigen4 * 100, digits = 1)
bray_rel_eigen5 <- bray_rel_eigens[5]
bray_rel_eigen5_percent <- round(bray_rel_eigen5 * 100, digits = 1)
bray_axis1 <- paste("PCoA 1:",bray_rel_eigen1_percent,"%")
bray_axis2 <- paste("PCoA 2:",bray_rel_eigen2_percent,"%")
bray_axis3 <- paste("PCoA 3:",bray_rel_eigen3_percent,"%")
bray_axis4 <- paste("PCoA 4:",bray_rel_eigen4_percent,"%")
PCoA_title <- paste("Bray-Curtis,",ntaxa(physeq.scale),"OTUs")
pcoa_exp_trt <- ggplot(physeq.pcoa.df, aes(Axis.1, Axis.2, color = TRT,fill = TRT)) +
xlab(bray_axis1) +
ylab(bray_axis2) +
geom_point(alpha=0.9) +
theme_classic() +
scale_fill_manual(values = c("#00B050","grey"),"Treatment", labels = c("Alone", "Competition"))+
scale_color_manual(values = c("#00B050","grey"),"Treatment", labels = c("Alone", "Competition"))+
stat_ellipse(geom = "polygon", alpha = 1/6, aes(fill =TRT))+
Tx+
theme(axis.text.x = element_text(angle=45),axis.text=element_text(color="black",size=15,vjust = 0.5,hjust=1))
# scale_fill_discrete(name = "Treatment", labels = c("Alone", "Competition"))+
# scale_color_discrete(name = "Treatment", labels = c("Alone", "Competition"))
pcoa_exp_trtA <- ggplot(physeq.pcoa.df, aes(Axis.3, Axis.4, color = TRT,fill = TRT)) +
xlab(bray_axis3) +
ylab(bray_axis4) +
geom_point(alpha=0.9) +
theme_classic() +
scale_fill_manual(values = GoldGrey,"Treatment", labels = c("Alone", "Competition"))+
scale_color_manual(values = GoldGrey,"Treatment", labels = c("Alone", "Competition"))+
stat_ellipse(geom = "polygon", alpha = 1/6, aes(fill =TRT))+
Tx
pcoa_exp_sp <- ggplot(physeq.pcoa.df, aes(Axis.1, Axis.2, color = Species,fill = Species)) +
xlab("") +
ylab(bray_axis2) +
geom_point(alpha=0.9) +
theme_classic() +
scale_fill_manual(values = GreenBlue,"Species", labels = c("I. hederacea", "I. purpurea"))+
scale_color_manual(values = GreenBlue,"Species", labels = c("I. hederacea", "I. purpurea"))+
stat_ellipse(geom = "polygon", alpha = 1/6, aes(fill =Species))+
Tx
pcoa_exp_spA <- ggplot(physeq.pcoa.df, aes(Axis.3, Axis.4, color = Species,fill = Species)) +
xlab("") +
ylab(bray_axis4) +
geom_point(alpha=0.9) +
theme_classic()+
scale_fill_manual(values = GreenBlue,"Species", labels = c("I. hederacea", "I. purpurea"))+
scale_color_manual(values = GreenBlue,"Species", labels = c("I. hederacea", "I. purpurea"))+
stat_ellipse(geom = "polygon", alpha = 1/6, aes(fill =Species))+
Tx
dev.off()FALSE null device
FALSE 1A=ggarrange(pcoa_exp_trt,pcoa_exp_trtA,common.legend = T,labels=c("C","D"),font.label = list(size = 15, color = "black", face =
"plain"),hjust = -8,vjust=1)
B=ggarrange(pcoa_exp_sp,pcoa_exp_spA,common.legend = T,labels=c("A","B"),font.label = list(size = 15, color = "black", face =
"plain"),hjust = -8,vjust=1)
MainFig=ggarrange(B,A,nrow=2)
annotate_figure(MainFig,
top = text_grob(PCoA_title, face = "plain", size = 25,lineheight = 2)
)physeq.pcoa.df$TrtSp=paste(physeq.pcoa.df$TRT,physeq.pcoa.df$Species,sep="")
p <- plot_ly(physeq.pcoa.df, x = ~Axis.1, y = ~Axis.2, z = ~Axis.3, color = ~TrtSp) %>%
add_markers() %>%
layout(scene = list(xaxis = list(title = bray_axis1),
yaxis = list(title = bray_axis2),
zaxis = list(title = bray_axis3)))
p1 <- plot_ly(physeq.pcoa.df, x = ~Axis.1, y = ~Axis.2, z = ~Axis.4, color = ~Species) %>%
add_markers() %>%
layout(scene = list(xaxis = list(title = bray_axis1),
yaxis = list(title = bray_axis2),
zaxis = list(title = bray_axis4)))
p3 <- plot_ly(physeq.pcoa.df, x = ~Axis.1, y = ~Axis.2, z = ~Axis.4, color = ~Species) %>%
add_markers() %>%
layout(scene = list(xaxis = list(title = bray_axis1),
yaxis = list(title = bray_axis3),
zaxis = list(title = bray_axis4)))## All experiment, add variable treatment, then species
sampledf <- data.frame(sample_data(physeq.scale))
sampledf=subset(sampledf,sampledf$TRT=="Alone"|sampledf$TRT=="Inter")
## Subsample by species
physeq.purp=subset_samples(physeq.scale, Species == "Ip")
physeq.hed=subset_samples(physeq.scale, Species != "Ip")
## Subsample within competition
physeq.comp=subset_samples(physeq.scale, TRT=="Inter")
# Calculate bray curtis for experimental samples only
physeq.bray <- phyloseq::distance(physeq = physeq.scale, method = "bray") # acrosss species and treatment
physeq.bray2 <- phyloseq::distance(physeq = physeq.purp, method = "bray") # within Ipurp
physeq.bray2b <- phyloseq::distance(physeq = physeq.hed, method = "bray") # within Ipurp
physeq.bray3 <- phyloseq::distance(physeq = physeq.comp, method = "bray") # within competition
sampledf$Comp=sub(".*\\-","",sampledf$Combos)
# Adonis test for treatment, across species
adonis(physeq.bray ~ TRT, data = sampledf)FALSE
FALSE Call:
FALSE adonis(formula = physeq.bray ~ TRT, data = sampledf)
FALSE
FALSE Permutation: free
FALSE Number of permutations: 999
FALSE
FALSE Terms added sequentially (first to last)
FALSE
FALSE Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
FALSE TRT 1 0.0291 0.029087 0.89564 0.00521 0.494
FALSE Residuals 171 5.5533 0.032476 0.99479
FALSE Total 172 5.5824 1.00000FALSE Df Sum Sq Mean Sq F N.Perm Pr(>F)
FALSE Groups 1 0.004538395 0.004538395 1.602334 999 0.196
FALSE Residuals 171 0.484334618 0.002832366 NA NA NA# Adonis test for treatment, WITHIN species
adonis(physeq.bray2 ~ TRT+Block, data = sampledf%>%filter(Species=="Ip")) # No treatment effect on bray distancesFALSE
FALSE Call:
FALSE adonis(formula = physeq.bray2 ~ TRT + Block, data = sampledf %>% filter(Species == "Ip"))
FALSE
FALSE Permutation: free
FALSE Number of permutations: 999
FALSE
FALSE Terms added sequentially (first to last)
FALSE
FALSE Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
FALSE TRT 1 0.0258 0.025835 0.8460 0.00796 0.549
FALSE Block 3 0.3189 0.106312 3.4813 0.09826 0.001 ***
FALSE Residuals 95 2.9011 0.030538 0.89378
FALSE Total 99 3.2459 1.00000
FALSE ---
FALSE Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1FALSE Df Sum Sq Mean Sq F N.Perm Pr(>F)
FALSE Groups 1 0.004538395 0.004538395 1.602334 999 0.215
FALSE Residuals 171 0.484334618 0.002832366 NA NA NA# Adonis test for treatment, WITHIN species
adonis(physeq.bray2 ~ TRT+Block*ML, data = sampledf%>%filter(Species=="Ip")) # No treatment effect on bray distancesFALSE
FALSE Call:
FALSE adonis(formula = physeq.bray2 ~ TRT + Block * ML, data = sampledf %>% filter(Species == "Ip"))
FALSE
FALSE Permutation: free
FALSE Number of permutations: 999
FALSE
FALSE Terms added sequentially (first to last)
FALSE
FALSE Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
FALSE TRT 1 0.0258 0.025835 0.8539 0.00796 0.543
FALSE Block 3 0.3189 0.106312 3.5139 0.09826 0.001 ***
FALSE ML 9 0.2367 0.026301 0.8693 0.07293 0.757
FALSE Block:ML 22 0.7281 0.033097 1.0939 0.22432 0.195
FALSE Residuals 64 1.9363 0.030254 0.59653
FALSE Total 99 3.2459 1.00000
FALSE ---
FALSE Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1adonis(physeq.bray2b ~ Block*ML, data = sampledf%>%filter(Species!="Ip")) # No treatment effect on bray distancesFALSE
FALSE Call:
FALSE adonis(formula = physeq.bray2b ~ Block * ML, data = sampledf %>% filter(Species != "Ip"))
FALSE
FALSE Permutation: free
FALSE Number of permutations: 999
FALSE
FALSE Terms added sequentially (first to last)
FALSE
FALSE Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
FALSE Block 3 0.22002 0.073340 2.49402 0.09648 0.001 ***
FALSE ML 4 0.07412 0.018530 0.63013 0.03250 0.975
FALSE Block:ML 9 0.33957 0.037730 1.28305 0.14890 0.035 *
FALSE Residuals 56 1.64675 0.029406 0.72211
FALSE Total 72 2.28046 1.00000
FALSE ---
FALSE Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Adonis test for species
set.seed(7L)
adonis(physeq.bray3 ~ Species+Block*ML, data = sampledf%>%filter(TRT=="Inter"))FALSE
FALSE Call:
FALSE adonis(formula = physeq.bray3 ~ Species + Block * ML, data = sampledf %>% filter(TRT == "Inter"))
FALSE
FALSE Permutation: free
FALSE Number of permutations: 999
FALSE
FALSE Terms added sequentially (first to last)
FALSE
FALSE Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
FALSE Species 1 0.0528 0.052832 1.7517 0.01095 0.049 *
FALSE Block 3 0.3790 0.126343 4.1890 0.07855 0.001 ***
FALSE ML 13 0.3674 0.028262 0.9370 0.07614 0.665
FALSE Block:ML 32 1.1304 0.035325 1.1712 0.23427 0.050 *
FALSE Residuals 96 2.8955 0.030161 0.60008
FALSE Total 145 4.8251 1.00000
FALSE ---
FALSE Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1FALSE Df Sum Sq Mean Sq F N.Perm Pr(>F)
FALSE Groups 1 0.003812412 0.003812412 1.279186 999 0.246
FALSE Residuals 144 0.429169301 0.002980342 NA NA NA# # # # # # # # # # # # # # # # # # # # #
# ACROSS SAMPLES
amova(physeq.bray ~ TRT, data = sampledf) # Across all samples##
## Analysis of Molecular Variance
##
## Call: amova(formula = physeq.bray ~ TRT, data = sampledf)
##
## SSD MSD df
## TRT 0.02908666 0.02908666 1
## Error 5.55333864 0.03247566 171
## Total 5.58242529 0.03245596 172
##
## Variance components:
## sigma2 P.value
## TRT -7.4366e-05 0.4895
## Error 3.2476e-02
##
## Phi-statistics:
## TRT.in.GLOBAL
## -0.002295142
##
## Variance coefficients:
## a
## 45.57225## Warning in amova(physeq.bray ~ Species, data = sampledf): elements in the rhs of
## the formula are not all factors##
## Analysis of Molecular Variance
##
## Call: amova(formula = physeq.bray ~ Species, data = sampledf)
##
## SSD MSD df
## Species 0.05608391 0.05608391 1
## Error 5.52634139 0.03231779 171
## Total 5.58242529 0.03245596 172
##
## Variance components:
## sigma2 P.value
## Species 0.00028161 0.0639
## Error 0.03231779
##
## Phi-statistics:
## Species.in.GLOBAL
## 0.008638573
##
## Variance coefficients:
## a
## 84.39306# # # # # # # # # # # # # # # # # # # # #
# Subsample for within I. purpurea only
# # # # # # # # # # # # # # # # # # # # #
physeq.Purp <- subset_samples(physeq.scale, Species == "Ip")
sampledf.Purp<- data.frame(sample_data(physeq.Purp))
# Calculate bray curtis for summer samples only
physeq.Purp.bray <- phyloseq::distance(physeq = physeq.Purp, method = "bray")
amova(physeq.Purp.bray ~ TRT, data = sampledf.Purp) # Across all samples##
## Analysis of Molecular Variance
##
## Call: amova(formula = physeq.Purp.bray ~ TRT, data = sampledf.Purp)
##
## SSD MSD df
## TRT 0.02583514 0.02583514 1
## Error 3.22005058 0.03285766 98
## Total 3.24588571 0.03278672 99
##
## Variance components:
## sigma2 P.value
## TRT -0.00017815 0.6184
## Error 0.03285766
##
## Phi-statistics:
## TRT.in.GLOBAL
## -0.005451311
##
## Variance coefficients:
## a
## 39.42# # # # # # # # # # # # # # # # # # # # #
# Subsample for within competition
# # # # # # # # # # # # # # # # # # # # #
physeq.Comp <- subset_samples(physeq.scale, TRT=="Inter")
sampledf.Comp<- data.frame(sample_data(physeq.Comp))
# Calculate bray curtis for summer samples only
physeq.Comp.bray <- phyloseq::distance(physeq = physeq.Comp, method = "bray")
amova(physeq.Comp.bray ~ Species, data = sampledf.Comp) # marginal species differences## Warning in amova(physeq.Comp.bray ~ Species, data = sampledf.Comp): elements in
## the rhs of the formula are not all factors##
## Analysis of Molecular Variance
##
## Call: amova(formula = physeq.Comp.bray ~ Species, data = sampledf.Comp)
##
## SSD MSD df
## Species 0.05283239 0.05283239 1
## Error 4.77230564 0.03314101 144
## Total 4.82513803 0.03327681 145
##
## Variance components:
## sigma2 P.value
## Species 0.00026974 0.0979
## Error 0.03314101
##
## Phi-statistics:
## Species.in.GLOBAL
## 0.008073593
##
## Variance coefficients:
## a
## 73Test for differently abundant OTUs
Visualize the different groups at the family level
# Check for 'core' microbiome members as the phylum level which taxa are present
# at 1 % overall abundance and at least 75% of samples
PhylumGlom<-tax_glom(physeq.Purp,taxrank="Phylum")
FamGlom<-tax_glom(physeq.Purp,taxrank="Family")
ClassGlom<-tax_glom(physeq.Purp,taxrank="Class")
coreTaxa = filter_taxa(PhylumGlom, function(x) sum(x > 1) > (0.75 * length(x)), TRUE)
coreTaxaFamily = filter_taxa(FamGlom, function(x) sum(x > 1) > (0.75 * length(x)), TRUE)
## Plot at phylum level
physeq1_phylumAlone <- coreTaxa %>%
subset_samples(TRT=="Alone")%>%
transform_sample_counts(function(x) {x/sum(x)} ) %>% # Transform to rel. abundance
psmelt()
physeq1_phylumComp <- coreTaxa %>%
subset_samples(TRT!="Alone")%>%
transform_sample_counts(function(x) {x/sum(x)} ) %>% # Transform to rel. abundance
psmelt()
physeq1_phylum<-rbind(physeq1_phylumAlone,physeq1_phylumComp)
# Melt to long format
physeq1_phylum=physeq1_phylum[order(physeq1_phylum$Phylum),]
#colnames(physeq1_phylum)[13]="Phylum"
# Sort data frame alphabetically by phylum
# Set colors for plotting
phylum_colors <- c(
"#CBD588", "#5F7FC7", "orange","#DA5724", "#508578", "#CD9BCD",
"#AD6F3B", "#673770","#D14285", "#652926", "#C84248",
"#8569D5", "#5E738F","#D1A33D", "#8A7C64", "#599861"
)
#colnames(physeq1_phylum)[which(names(physeq1_phylum)%in%"Rank2")]="Phylum"
# Plot
ggplot(physeq1_phylum, aes(x = TRT, y = Abundance, fill = Phylum)) +
geom_bar(stat = "identity",position='dodge')+
#scale_fill_manual(values = phylum_colors)+
theme(axis.title.x = element_blank()) +
ylab("Relative Abundance (Phyla > 75 %) \n") +
ggtitle("Phylum Composition \n Bacterial Communities by Sampling per Treatment") +
theme_classic()+
ylab("Relative Abundance")
Testing if different at the phylum level
PhlyaList<-as.list(unique(physeq1_phylum$Phylum))
KrusMicrTest<-function(Microbe){
Result=kruskal.test(Abundance ~ TRT, data = physeq1_phylum[which(physeq1_phylum$Phylum==Microbe),])
ResDf=data.frame("ChiSq"=Result$statistic,"Pval"=Result$p.value,"Phylum"=paste(Microbe))
return(ResDf)
}
AllResults=lapply(PhlyaList,KrusMicrTest)
KruskalRes=do.call('rbind',AllResults)Family level
# Family level
physeq1_FamilyAlone <- coreTaxaFamily %>%
subset_samples(TRT=="Alone")%>%
transform_sample_counts(function(x) {x/sum(x)} ) %>% # Transform to rel. abundance
psmelt() # Melt to long format
physeq1_FamilyComp <- coreTaxaFamily %>%
subset_samples(TRT!="Alone")%>%
transform_sample_counts(function(x) {x/sum(x)} ) %>% # Transform to rel. abundance
psmelt()
physeq1_Family<-rbind(physeq1_FamilyAlone,physeq1_FamilyComp)
FamList<-as.list(unique(physeq1_Family$Family))
KrusMicrTest<-function(Microbe){
Result=kruskal.test(Abundance ~ TRT, data = physeq1_Family[which(physeq1_Family$Family==Microbe),])
ResDf=data.frame("ChiSq"=Result$statistic,"Pval"=Result$p.value,"Family"=paste(Microbe))
return(ResDf)
}
AllResultsFamily=lapply(FamList,KrusMicrTest)
KruskalResFamily=do.call('rbind',AllResultsFamily)
KruskalResFamily%>%filter(Pval<0.055)## ChiSq Pval Family
## 1 5.192655 0.022682540 Subgroup_2_fa
## 2 3.904351 0.048161234 Gaiellaceae
## 3 3.752445 0.052730323 Lineage_IIa_fa
## 4 4.186783 0.040740338 SM2D12
## 5 4.509080 0.033715377 AKYG1722
## 6 3.904351 0.048161234 Microtrichaceae
## 7 8.682062 0.003213572 A0839Alpha diversity
# Remove sample with less than 20K reads, this looks WAAAY off
# Rarify first
ps.rarefied=rarefy_even_depth(physeq1,rngseed=1,sample.size=min(sample_sums(physeq1)),replace=F)
plot_richness(ps.rarefied,x="TRT",measures=c("Observed","Shannon"))+
geom_boxplot()+
theme_classic()
Alpha Diversity
Note: Measures of alpha-diversity
Inverse Simpson it is an indication of the richness in a community with uniform evenness that would have the same level of diversity. So while measures such as the Shannon index are somewhat abstract, the inverse of the Simpson index has some biological interpretation. Other advantages of the Simpson-based metrics are that they do not tend to be as affected by sampling effort as the Shannon index.
Species richness is simply a count of species, and it does not take into account the abundances of the species or their relative abundance distributions.
Simpson’s Diversity Index is a measure of diversity which takes into account the number of species present, as well as the relative abundance of each species. As species richness and evenness increase,so diversity increases.
### I commented out the subsampling to save time. The matrices produced were saved and then reoponed from their tab delmited formats into corresponding matrices.
set.seed(3)
r <- rarefy_even_depth(physeq1, sample.size = n, verbose = FALSE, replace = TRUE)
## Calculate richness
rich <- as.numeric(as.matrix(estimate_richness(r, measures = "Observed")))
## Calculate Inverse Simpson
simp <- as.numeric(as.matrix(estimate_richness(r, measures = "InvSimpson")))
sim<- as.numeric(as.matrix(estimate_richness(r, measures = "Simpson")))
s <- rarefy_even_depth(physeq1, sample.size = n, verbose = FALSE, replace = TRUE)
shan <- as.numeric(as.matrix(estimate_richness(r, measures = "Shannon")))
InvSimp=simp# Create a new dataframe to hold the means and standard deviations of richness estimates
length(rich)## [1] 173Sample_ID <- sample_names(physeq1)
Block <-sample_data(physeq1)$Block
Species <-sample_data(physeq1)$Species
TRT <-sample_data(physeq1)$TRT
Combos <-sample_data(physeq1)$Combos
ML <-sample_data(physeq1)$ML
alpha=data.frame(Sample_ID,ML,Block,TRT,Species,Combos,rich,InvSimp,sim,shan)
alpha$even=alpha$shan/alpha$rich
# DO VIOLIN PLOT HERE!!!
p=ggplot(alpha%>%filter(TRT=="Inter"), aes(x=Species, y=rich)) +
geom_violin(trim=FALSE,aes(fill=Species),alpha=0.3)+
geom_dotplot(binaxis='y', stackdir='center', dotsize=1,aes(color=Species,fill=Species))+
theme_classic()+
scale_color_brewer(palette = "Paired")+
scale_fill_brewer(palette = "Paired")+
ggtitle("Mean Species Richness")
q=ggplot(alpha%>%filter(TRT=="Inter"), aes(x=Species, y=InvSimp)) +
geom_violin(trim=FALSE,aes(fill=Species),alpha=0.3)+
geom_dotplot(binaxis='y', stackdir='center', dotsize=1,aes(color=Species,fill=Species))+
theme_classic()+
scale_color_brewer(palette = "Paired")+
scale_fill_brewer(palette = "Paired")+
ggtitle("Mean Species Inverse Simpson")+
ylab("")
t=ggplot(alpha%>%filter(TRT=="Inter"), aes(x=Species, y=sim)) +
geom_violin(trim=FALSE,aes(fill=Species),alpha=0.3)+
geom_dotplot(binaxis='y', stackdir='center', dotsize=1,aes(color=Species,fill=Species))+
theme_classic()+
scale_color_brewer(palette = "Paired")+
scale_fill_brewer(palette = "Paired")+
ggtitle("Mean Simpson")+
ylab("")
v=ggplot(alpha%>%filter(TRT=="Inter"), aes(x=Species, y=even)) +
geom_violin(trim=FALSE,aes(fill=Species),alpha=0.3)+
geom_dotplot(binaxis='y', stackdir='center', dotsize=1,aes(color=Species,fill=Species))+
theme_classic()+
scale_color_brewer(palette = "Paired")+
scale_fill_brewer(palette = "Paired")+
ggtitle("Mean Evenness")+
ylab("")
ggarrange(p,q,t,v,common.legend=T,ncol=2,nrow=2)## `stat_bindot()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bindot()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bindot()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bindot()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bindot()` using `bins = 30`. Pick better value with `binwidth`.
### Treatment
pT=ggplot(alpha%>%filter(Species=="Ip"), aes(x=TRT, y=rich)) +
geom_violin(trim=FALSE,aes(fill=TRT),alpha=0.3)+
geom_dotplot(binaxis='y', stackdir='center', dotsize=1,aes(color=TRT,fill=TRT))+
theme_classic()+
scale_color_manual(values=c("#B2DF8A","#fee090"))+
scale_fill_manual(values=c("#B2DF8A","#fee090"))+
ggtitle("Mean Treatment Richness")
qT=ggplot(alpha%>%filter(Species=="Ip"), aes(x=TRT, y=InvSimp)) +
geom_violin(trim=FALSE,aes(fill=TRT),alpha=0.3)+
geom_dotplot(binaxis='y', stackdir='center', dotsize=1,aes(color=TRT,fill=TRT))+
theme_classic()+
scale_color_manual(values = c("#B2DF8A","#fee090"))+
scale_fill_manual(values = c("#B2DF8A","#fee090"))+
ggtitle("Mean Treatment Inverse Simpson")+
ylab(" ")
ggarrange(pT,qT,common.legend=T)## `stat_bindot()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bindot()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bindot()` using `bins = 30`. Pick better value with `binwidth`.
Test for differences
# first check for normality. To test for normalcy statistically, we can run the Shapiro-Wilk test of normality.
shapiro.test(alpha$rich) # Not normalFALSE
FALSE Shapiro-Wilk normality test
FALSE
FALSE data: alpha$rich
FALSE W = 0.98897, p-value = 0.1974FALSE
FALSE Shapiro-Wilk normality test
FALSE
FALSE data: alpha$even
FALSE W = 0.97645, p-value = 0.004898FALSE
FALSE Shapiro-Wilk normality test
FALSE
FALSE data: alpha$sim
FALSE W = 0.90086, p-value = 2.238e-09
# Run the ANOVA and save it as an object
# Test for species within competition
aov.Richness = aov(rich~Species+Block,alpha%>%filter(TRT=="Inter"))
aov.simpsonInv = aov(InvSimp~Species+Block,alpha%>%filter(TRT=="Inter"))
aov.simpson = aov(sim~Species+Block,alpha%>%filter(TRT=="Inter"))
aov.evenness = aov(even~Species+Block,alpha%>%filter(TRT=="Inter"))
aov.shannon = aov(shan~Species+Block,alpha%>%filter(TRT=="Inter"))
#Call for the summary of that ANOVA, which will include P-values
summary(aov.Richness)FALSE Df Sum Sq Mean Sq F value Pr(>F)
FALSE Species 1 144 144 0.184 0.668475
FALSE Block 3 15795 5265 6.733 0.000281 ***
FALSE Residuals 141 110255 782
FALSE ---
FALSE Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1FALSE Df Sum Sq Mean Sq F value Pr(>F)
FALSE Species 1 145 144.7 1.676 0.19752
FALSE Block 3 1038 345.9 4.007 0.00898 **
FALSE Residuals 141 12172 86.3
FALSE ---
FALSE Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1FALSE Df Sum Sq Mean Sq F value Pr(>F)
FALSE Species 1 0.000032 3.249e-05 0.499 0.4810
FALSE Block 3 0.000487 1.623e-04 2.493 0.0626 .
FALSE Residuals 141 0.009177 6.509e-05
FALSE ---
FALSE Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1FALSE Df Sum Sq Mean Sq F value Pr(>F)
FALSE Species 1 2.940e-07 2.941e-07 1.732 0.190243
FALSE Block 3 3.552e-06 1.184e-06 6.974 0.000208 ***
FALSE Residuals 141 2.393e-05 1.697e-07
FALSE ---
FALSE Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1FALSE Df Sum Sq Mean Sq F value Pr(>F)
FALSE Species 1 0.009 0.00925 0.296 0.58710
FALSE Block 3 0.370 0.12345 3.955 0.00961 **
FALSE Residuals 141 4.402 0.03122
FALSE ---
FALSE Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# No significant differences
# Test for treatment within I. purpurea
alpha.purp<-alpha%>%filter(Species=="Ip")
aov.Richness = lm(rich~TRT+Block,alpha.purp)
aov.simpsonInv = lm(InvSimp~TRT+Block,alpha.purp)
aov.simpson = lm(sim~TRT+Block,alpha.purp)
aov.evenness = lm(even~TRT+Block,alpha.purp)
aov.shannon = lm(shan~TRT+Block,alpha.purp)
#Call for the summary of that ANOVA, which will include P-values
anova(aov.Richness)FALSE Analysis of Variance Table
FALSE
FALSE Response: rich
FALSE Df Sum Sq Mean Sq F value Pr(>F)
FALSE TRT 1 796 796.2 0.8580 0.356657
FALSE Block 3 15895 5298.2 5.7094 0.001229 **
FALSE Residuals 95 88158 928.0
FALSE ---
FALSE Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1FALSE Analysis of Variance Table
FALSE
FALSE Response: InvSimp
FALSE Df Sum Sq Mean Sq F value Pr(>F)
FALSE TRT 1 0.3 0.33 0.0038 0.950870
FALSE Block 3 1064.0 354.66 4.1296 0.008463 **
FALSE Residuals 95 8158.8 85.88
FALSE ---
FALSE Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1FALSE Analysis of Variance Table
FALSE
FALSE Response: sim
FALSE Df Sum Sq Mean Sq F value Pr(>F)
FALSE TRT 1 0.0000215 2.1498e-05 0.3573 0.55143
FALSE Block 3 0.0005168 1.7225e-04 2.8629 0.04084 *
FALSE Residuals 95 0.0057158 6.0166e-05
FALSE ---
FALSE Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1FALSE Analysis of Variance Table
FALSE
FALSE Response: even
FALSE Df Sum Sq Mean Sq F value Pr(>F)
FALSE TRT 1 1.1710e-07 1.1708e-07 0.5761 0.449707
FALSE Block 3 2.9070e-06 9.6899e-07 4.7684 0.003857 **
FALSE Residuals 95 1.9305e-05 2.0321e-07
FALSE ---
FALSE Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# No significant differences
# Model accross species and treatment
aov.Richness = aov(rich~TRT+Species+Block,alpha)
aov.simpsonInv = aov(InvSimp~TRT+Species+Block,alpha)
aov.simpson = aov(sim~TRT+Species+Block,alpha)
aov.evenness = aov(even~TRT+Species+Block,alpha)
aov.shannon = aov(shan~TRT+Species+Block,alpha)
#Call for the summary of that ANOVA, which will include P-values
anova(aov.Richness)FALSE Analysis of Variance Table
FALSE
FALSE Response: rich
FALSE Df Sum Sq Mean Sq F value Pr(>F)
FALSE TRT 1 655 655.2 0.8179 0.3671
FALSE Species 1 144 144.0 0.1797 0.6721
FALSE Block 3 20181 6726.9 8.3964 3.13e-05 ***
FALSE Residuals 167 133794 801.2
FALSE ---
FALSE Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1FALSE Analysis of Variance Table
FALSE
FALSE Response: InvSimp
FALSE Df Sum Sq Mean Sq F value Pr(>F)
FALSE TRT 1 17.1 17.11 0.2112 0.646446
FALSE Species 1 144.7 144.71 1.7857 0.183267
FALSE Block 3 1089.9 363.31 4.4832 0.004694 **
FALSE Residuals 167 13533.5 81.04
FALSE ---
FALSE Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1FALSE Analysis of Variance Table
FALSE
FALSE Response: sim
FALSE Df Sum Sq Mean Sq F value Pr(>F)
FALSE TRT 1 0.0000524 5.2377e-05 0.8799 0.34958
FALSE Species 1 0.0000325 3.2494e-05 0.5459 0.46104
FALSE Block 3 0.0005244 1.7480e-04 2.9365 0.03494 *
FALSE Residuals 167 0.0099410 5.9527e-05
FALSE ---
FALSE Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1FALSE Analysis of Variance Table
FALSE
FALSE Response: even
FALSE Df Sum Sq Mean Sq F value Pr(>F)
FALSE TRT 1 2.3600e-08 2.3610e-08 0.1311 0.7177
FALSE Species 1 2.9410e-07 2.9407e-07 1.6328 0.2031
FALSE Block 3 4.4640e-06 1.4880e-06 8.2619 3.707e-05 ***
FALSE Residuals 167 3.0077e-05 1.8010e-07
FALSE ---
FALSE Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# summary(aov.shannon)
# Boxplot
ggplot(alpha%>%filter(Species=="Ip"),aes(TRT,rich))+
geom_boxplot()+
theme_bw()+
ylab("Richness")+
xlab("")+
scale_x_discrete(labels=c("Alone","Competition"))+
theme(axis.text.x = element_text(vjust = -1),axis.text=element_text(size=20),axis.title=element_text(size=30),axis.title.x = element_text(vjust=-1))+
Margin
ggplot(alpha%>%filter(Species=="Ip"),aes(TRT,even))+
geom_boxplot()+
theme_bw()+
ylab("Evenness")+
xlab("")+
scale_x_discrete(labels=c("Alone","Competition"))+
theme(axis.text.x = element_text(vjust = -1),axis.text=element_text(size=20),axis.title=element_text(size=30),axis.title.x = element_text(vjust=-1))+
Margin
ggplot(alpha%>%filter(Species=="Ip"),aes(TRT,sim))+
geom_boxplot()+
theme_bw()+
ylab("Simpson")+
xlab("")+
scale_x_discrete(labels=c("Alone","Competition"))+
theme(axis.text.x = element_text(vjust = -1),axis.text=element_text(size=20),axis.title=element_text(size=30),axis.title.x = element_text(vjust=-1))+
Margin
ggplot(alpha%>%filter(Species=="Ip"),aes(TRT,InvSimp))+
geom_boxplot()+
theme_bw()+
ylab("Inverse Simpson")+
xlab("")+
scale_x_discrete(labels=c("Alone","Competition"))+
theme(axis.text.x = element_text(vjust = -1),axis.text=element_text(size=20),axis.title=element_text(size=30),axis.title.x = element_text(vjust=-1))+
Margin
Linear mixed models
# Test for treatment within I. purpurea
RichLmm = lmer(rich~TRT+Block+(1|Block:ML),alpha%>%filter(Species=="Ip"))
InvLmm = lmer(InvSimp~TRT+Block+(1|Block:ML),alpha%>%filter(Species=="Ip"))
SimLmm = lmer(sim~TRT+Block+(1|Block:ML),alpha%>%filter(Species=="Ip"))
EvenLmm = lmer(even~TRT+Block+(1|Block:ML),alpha%>%filter(Species=="Ip"))## boundary (singular) fit: see ?isSingular## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## TRT 1129.9 1129.9 1 87.699 1.2493 0.266729
## Block 14252.4 4750.8 3 27.782 5.2530 0.005343 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## rich ~ TRT + Block + (1 | Block:ML)
## npar logLik AIC LRT Df Pr(>Chisq)
## <none> 7 -467.25 948.49
## (1 | Block:ML) 6 -467.29 946.58 0.089955 1 0.7642## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## TRT 2.27 2.269 1 80.987 0.0301 0.86273
## Block 706.55 235.516 3 23.542 3.1234 0.04503 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## InvSimp ~ TRT + Block + (1 | Block:ML)
## npar logLik AIC LRT Df Pr(>Chisq)
## <none> 7 -353.56 721.12
## (1 | Block:ML) 6 -354.24 720.48 1.3546 1 0.2445## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## TRT 0.00002586 2.5859e-05 1 78.161 0.5091 0.4776
## Block 0.00031682 1.0561e-04 3 22.168 2.0793 0.1319## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## sim ~ TRT + Block + (1 | Block:ML)
## npar logLik AIC LRT Df Pr(>Chisq)
## <none> 7 319.86 -625.72
## (1 | Block:ML) 6 318.90 -625.80 1.9211 1 0.1657## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## TRT 1.484e-07 1.4840e-07 1 95 0.7303 0.394939
## Block 2.907e-06 9.6899e-07 3 95 4.7684 0.003857 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## even ~ TRT + Block + (1 | Block:ML)
## npar logLik AIC LRT Df Pr(>Chisq)
## <none> 7 589.21 -1164.4
## (1 | Block:ML) 6 589.21 -1166.4 0 1 1Continous data (root traits, leaf number)
Here, I correlate leaf number to OTUs with at least 5% relative abundance in at least one sample in our data set.
Preliminary test with roots
RootData=read.csv("~/Google Drive File Stream/My Drive/Baucom Lab /Chapter3MicrobiomeMothur/Microbiome_2018/DataSets/MothurOutput_Mock_Microbiome/Microbiome_Output/RootTraits_PCs.csv")
RootAlphaObs=merge(alpha,RootData[c("Sample_ID","PC1","PC2","PC3","PC4")])
SimpPC1=lm(sim~PC1+Species+TRT+Block,RootAlphaObs)
summary(SimpPC1)##
## Call:
## lm(formula = sim ~ PC1 + Species + TRT + Block, data = RootAlphaObs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.029870 -0.003809 0.002029 0.005361 0.012419
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.9769760 0.0035609 274.366 <2e-16 ***
## PC1 0.0004790 0.0007839 0.611 0.5428
## SpeciesIp -0.0001971 0.0018501 -0.107 0.9154
## TRTInter -0.0031596 0.0023507 -1.344 0.1823
## Block2 -0.0031756 0.0067999 -0.467 0.6416
## Block3 -0.0051282 0.0069792 -0.735 0.4644
## Block4 -0.0041017 0.0019957 -2.055 0.0428 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.007975 on 89 degrees of freedom
## Multiple R-squared: 0.07918, Adjusted R-squared: 0.01711
## F-statistic: 1.276 on 6 and 89 DF, p-value: 0.2767##
## Call:
## lm(formula = InvSimp ~ PC1 + Species + TRT + Block, data = RootAlphaObs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -18.7250 -6.1683 0.8967 5.7030 25.1023
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 42.5076 4.0523 10.490 <2e-16 ***
## PC1 0.6858 0.8921 0.769 0.4441
## SpeciesIp 0.5410 2.1054 0.257 0.7978
## TRTInter -2.3764 2.6751 -0.888 0.3767
## Block2 -4.7350 7.7383 -0.612 0.5422
## Block3 -6.3293 7.9424 -0.797 0.4276
## Block4 -4.8285 2.2711 -2.126 0.0363 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.075 on 89 degrees of freedom
## Multiple R-squared: 0.0808, Adjusted R-squared: 0.01883
## F-statistic: 1.304 on 6 and 89 DF, p-value: 0.2637##
## Call:
## lm(formula = rich ~ PC1 + Species + TRT + Block, data = RootAlphaObs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -74.332 -14.939 4.194 19.133 48.387
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 468.360 12.361 37.890 <2e-16 ***
## PC1 2.629 2.721 0.966 0.3366
## SpeciesIp -5.247 6.422 -0.817 0.4162
## TRTInter -14.115 8.160 -1.730 0.0871 .
## Block2 -20.098 23.605 -0.851 0.3968
## Block3 -4.476 24.228 -0.185 0.8539
## Block4 -7.361 6.928 -1.063 0.2908
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 27.68 on 89 degrees of freedom
## Multiple R-squared: 0.1424, Adjusted R-squared: 0.08462
## F-statistic: 2.464 on 6 and 89 DF, p-value: 0.0299# Adjust p-value for multiple comparisons (1 for each PC used to test)
p.adjust((summary(RichPC1)$coefficients[2,4]), method = "bonferroni", n = 4) # still significant, corrected p-value:## [1] 1# 0.01158722
EvenPC1=lm(even~PC1+Species+TRT+Block,RootAlphaObs)
summary(EvenPC1)# Significant coefficient##
## Call:
## lm(formula = even ~ PC1 + Species + TRT + Block, data = RootAlphaObs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.166e-04 -2.610e-04 1.249e-05 2.338e-04 1.238e-03
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.015e-02 1.765e-04 57.516 <2e-16 ***
## PC1 -1.933e-05 3.887e-05 -0.497 0.620
## SpeciesIp 1.180e-04 9.172e-05 1.287 0.201
## TRTInter 1.512e-04 1.165e-04 1.297 0.198
## Block2 1.516e-04 3.371e-04 0.450 0.654
## Block3 -2.070e-04 3.460e-04 -0.598 0.551
## Block4 -4.765e-05 9.894e-05 -0.482 0.631
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0003954 on 89 degrees of freedom
## Multiple R-squared: 0.1476, Adjusted R-squared: 0.0901
## F-statistic: 2.568 on 6 and 89 DF, p-value: 0.02432 # Adjust p-value for multiple comparisons (1 for each PC used to test)
p.adjust((summary(EvenPC1)$coefficients[2,4]), method = "bonferroni", n = 4) # still significant, corrected p-value:## [1] 1##
## Call:
## lm(formula = sim ~ PC2 + Species + TRT + Block, data = RootAlphaObs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.028163 -0.004043 0.001313 0.005830 0.013279
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.736e-01 3.013e-03 323.175 <2e-16 ***
## PC2 -7.810e-04 5.118e-04 -1.526 0.131
## SpeciesIp -8.854e-05 1.798e-03 -0.049 0.961
## TRTInter -2.285e-03 2.357e-03 -0.969 0.335
## Block2 6.113e-04 3.135e-03 0.195 0.846
## Block3 4.825e-04 2.426e-03 0.199 0.843
## Block4 -1.923e-03 2.492e-03 -0.772 0.442
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.007889 on 89 degrees of freedom
## Multiple R-squared: 0.0989, Adjusted R-squared: 0.03815
## F-statistic: 1.628 on 6 and 89 DF, p-value: 0.1487##
## Call:
## lm(formula = InvSimp ~ PC2 + Species + TRT + Block, data = RootAlphaObs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -18.1610 -6.3592 0.0581 5.8878 26.1557
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 38.9405 3.4545 11.272 <2e-16 ***
## PC2 -0.6367 0.5869 -1.085 0.281
## SpeciesIp 0.7634 2.0611 0.370 0.712
## TRTInter -1.5637 2.7031 -0.578 0.564
## Block2 0.6192 3.5942 0.172 0.864
## Block3 0.7374 2.7818 0.265 0.792
## Block4 -3.1693 2.8575 -1.109 0.270
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.046 on 89 degrees of freedom
## Multiple R-squared: 0.08677, Adjusted R-squared: 0.02521
## F-statistic: 1.409 on 6 and 89 DF, p-value: 0.2198##
## Call:
## lm(formula = rich ~ PC2 + Species + TRT + Block, data = RootAlphaObs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -75.991 -15.616 2.075 19.857 46.962
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 448.8092 10.1991 44.005 < 2e-16 ***
## PC2 -4.7872 1.7326 -2.763 0.00696 **
## SpeciesIp -4.7202 6.0851 -0.776 0.43998
## TRTInter -8.8563 7.9807 -1.110 0.27011
## Block2 0.7606 10.6114 0.072 0.94302
## Block3 27.3263 8.2128 3.327 0.00128 **
## Block4 6.1108 8.4363 0.724 0.47075
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 26.71 on 89 degrees of freedom
## Multiple R-squared: 0.2019, Adjusted R-squared: 0.1481
## F-statistic: 3.752 on 6 and 89 DF, p-value: 0.002246 # Adjust p-value for multiple comparisons (1 for each PC used to test)
p.adjust((summary(RichPC2)$coefficients[2,4]), method = "bonferroni", n = 4) # still significant, corrected p-value:## [1] 0.02783753 # 0.04698757
EvenPC2=lm(even~PC2+Species+TRT+Block,RootAlphaObs)
summary(EvenPC2) # Significant coefficient##
## Call:
## lm(formula = even ~ PC2 + Species + TRT + Block, data = RootAlphaObs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.710e-04 -2.357e-04 -2.286e-05 2.430e-04 1.249e-03
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.036e-02 1.467e-04 70.584 < 2e-16 ***
## PC2 5.855e-05 2.492e-05 2.349 0.0210 *
## SpeciesIp 1.174e-04 8.754e-05 1.341 0.1832
## TRTInter 9.117e-05 1.148e-04 0.794 0.4292
## Block2 -5.041e-06 1.526e-04 -0.033 0.9737
## Block3 -4.877e-04 1.181e-04 -4.128 8.23e-05 ***
## Block4 -2.175e-04 1.214e-04 -1.792 0.0765 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0003842 on 89 degrees of freedom
## Multiple R-squared: 0.1951, Adjusted R-squared: 0.1408
## F-statistic: 3.595 on 6 and 89 DF, p-value: 0.003081 # Adjust p-value for multiple comparisons (1 for each PC used to test)
p.adjust((summary(EvenPC2)$coefficients[2,4]), method = "bonferroni", n = 4) # Not significant, corrected p-value:## [1] 0.08414438##
## Call:
## lm(formula = sim ~ PC3 + Species + TRT + Block, data = RootAlphaObs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.029375 -0.003550 0.001677 0.005369 0.011926
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.752e-01 2.789e-03 349.633 <2e-16 ***
## PC3 5.220e-04 5.981e-04 0.873 0.3851
## SpeciesIp 2.978e-05 1.812e-03 0.016 0.9869
## TRTInter -2.606e-03 2.374e-03 -1.098 0.2753
## Block2 9.475e-04 3.202e-03 0.296 0.7680
## Block3 -1.052e-03 2.217e-03 -0.474 0.6364
## Block4 -4.386e-03 1.970e-03 -2.226 0.0285 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.007958 on 89 degrees of freedom
## Multiple R-squared: 0.08317, Adjusted R-squared: 0.02136
## F-statistic: 1.346 on 6 and 89 DF, p-value: 0.2456##
## Call:
## lm(formula = InvSimp ~ PC3 + Species + TRT + Block, data = RootAlphaObs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -18.750 -5.725 0.898 5.296 24.783
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 40.1016 3.1796 12.612 <2e-16 ***
## PC3 0.5575 0.6818 0.818 0.4157
## SpeciesIp 0.8623 2.0654 0.418 0.6773
## TRTInter -1.7262 2.7059 -0.638 0.5252
## Block2 1.0062 3.6504 0.276 0.7835
## Block3 -0.5047 2.5274 -0.200 0.8422
## Block4 -5.2006 2.2461 -2.315 0.0229 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.072 on 89 degrees of freedom
## Multiple R-squared: 0.0816, Adjusted R-squared: 0.01968
## F-statistic: 1.318 on 6 and 89 DF, p-value: 0.2575##
## Call:
## lm(formula = rich ~ PC3 + Species + TRT + Block, data = RootAlphaObs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -72.850 -13.323 4.371 16.234 51.760
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 458.894 9.679 47.413 <2e-16 ***
## PC3 2.450 2.076 1.180 0.2410
## SpeciesIp -4.009 6.287 -0.638 0.5253
## TRTInter -11.388 8.237 -1.383 0.1703
## Block2 2.179 11.112 0.196 0.8450
## Block3 17.874 7.693 2.323 0.0224 *
## Block4 -8.845 6.837 -1.294 0.1991
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 27.61 on 89 degrees of freedom
## Multiple R-squared: 0.1468, Adjusted R-squared: 0.08927
## F-statistic: 2.552 on 6 and 89 DF, p-value: 0.02509##
## Call:
## lm(formula = even ~ PC3 + Species + TRT + Block, data = RootAlphaObs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.938e-04 -2.616e-04 4.780e-06 2.184e-04 1.217e-03
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.023e-02 1.383e-04 73.966 < 2e-16 ***
## PC3 -2.374e-05 2.965e-05 -0.801 0.42548
## SpeciesIp 1.088e-04 8.982e-05 1.212 0.22883
## TRTInter 1.268e-04 1.177e-04 1.078 0.28413
## Block2 -1.706e-05 1.587e-04 -0.107 0.91464
## Block3 -3.717e-04 1.099e-04 -3.382 0.00107 **
## Block4 -3.570e-05 9.768e-05 -0.365 0.71564
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0003945 on 89 degrees of freedom
## Multiple R-squared: 0.1513, Adjusted R-squared: 0.09409
## F-statistic: 2.645 on 6 and 89 DF, p-value: 0.02087### PC4
SimpPC4=lm(sim~PC4+Species+TRT+Block,RootAlphaObs)
summary(SimpPC4) # Significant coefficient##
## Call:
## lm(formula = sim ~ PC4 + Species + TRT + Block, data = RootAlphaObs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.023817 -0.004794 0.001242 0.005232 0.014173
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.9759837 0.0026241 371.935 < 2e-16 ***
## PC4 0.0022233 0.0007098 3.132 0.00235 **
## SpeciesIp 0.0011200 0.0017621 0.636 0.52665
## TRTInter -0.0025128 0.0022268 -1.128 0.26217
## Block2 -0.0012309 0.0030630 -0.402 0.68876
## Block3 -0.0020022 0.0021329 -0.939 0.35041
## Block4 -0.0059073 0.0019448 -3.038 0.00313 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.007584 on 89 degrees of freedom
## Multiple R-squared: 0.1671, Adjusted R-squared: 0.111
## F-statistic: 2.977 on 6 and 89 DF, p-value: 0.01072 # Adjust p-value for multiple comparisons (1 for each PC used to test)
p.adjust((summary(SimpPC4)$coefficients[2,4]), method = "bonferroni", n = 4) # still significant, corrected p-value:## [1] 0.009386743 # 0.00834712
SimpInvPC4=lm(InvSimp~PC4+Species+TRT+Block,RootAlphaObs)
summary(SimpInvPC4) # Significant coefficient##
## Call:
## lm(formula = InvSimp ~ PC4 + Species + TRT + Block, data = RootAlphaObs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -18.2849 -7.2012 0.6678 5.0565 26.9767
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 40.8792 3.0527 13.391 < 2e-16 ***
## PC4 1.9858 0.8257 2.405 0.01825 *
## SpeciesIp 1.8344 2.0499 0.895 0.37329
## TRTInter -1.7118 2.5906 -0.661 0.51047
## Block2 -1.0175 3.5633 -0.286 0.77590
## Block3 -1.3595 2.4813 -0.548 0.58512
## Block4 -6.5430 2.2625 -2.892 0.00481 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.823 on 89 degrees of freedom
## Multiple R-squared: 0.1312, Adjusted R-squared: 0.07258
## F-statistic: 2.239 on 6 and 89 DF, p-value: 0.04652 # Adjust p-value for multiple comparisons (1 for each PC used to test)
p.adjust((summary(SimpInvPC4)$coefficients[2,4]), method = "bonferroni", n = 4) # marginally significant, corrected p-value:## [1] 0.07299534##
## Call:
## lm(formula = rich ~ PC4 + Species + TRT + Block, data = RootAlphaObs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -76.083 -13.070 5.103 18.490 50.646
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 461.363 9.543 48.345 <2e-16 ***
## PC4 3.260 2.581 1.263 0.2099
## SpeciesIp -2.442 6.408 -0.381 0.7041
## TRTInter -12.517 8.098 -1.546 0.1257
## Block2 -2.457 11.139 -0.221 0.8260
## Block3 16.370 7.757 2.110 0.0376 *
## Block4 -10.769 7.073 -1.523 0.1314
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 27.58 on 89 degrees of freedom
## Multiple R-squared: 0.1487, Adjusted R-squared: 0.0913
## F-statistic: 2.591 on 6 and 89 DF, p-value: 0.02322##
## Call:
## lm(formula = even ~ PC4 + Species + TRT + Block, data = RootAlphaObs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.262e-04 -2.521e-04 -6.220e-06 2.183e-04 1.201e-03
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.021e-02 1.367e-04 74.719 < 2e-16 ***
## PC4 2.285e-05 3.697e-05 0.618 0.538201
## SpeciesIp 1.206e-04 9.179e-05 1.314 0.192340
## TRTInter 1.496e-04 1.160e-04 1.290 0.200393
## Block2 -1.454e-05 1.596e-04 -0.091 0.927613
## Block3 -3.795e-04 1.111e-04 -3.416 0.000959 ***
## Block4 -5.663e-05 1.013e-04 -0.559 0.577533
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0003951 on 89 degrees of freedom
## Multiple R-squared: 0.1488, Adjusted R-squared: 0.09147
## F-statistic: 2.594 on 6 and 89 DF, p-value: 0.02308Within species (root traits and alphadiv)
library(multcomp)
#summary(glht(SimpInvPC1, mcp(rank="Tukey")))
#################################################################
##################### SUBSET for I.purpurea #####################
#################################################################
RootAlphaPurp=droplevels(RootAlphaObs%>%filter(Species=="Ip"))
RootAlphaPurp$Comp=sub(".*\\-","",RootAlphaPurp$Combos)
SimpPC1=lm(sim~TRT+Block+PC1,RootAlphaPurp)
summary(SimpPC1)##
## Call:
## lm(formula = sim ~ TRT + Block + PC1, data = RootAlphaPurp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.027297 -0.003731 0.001626 0.005703 0.011295
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.977953 0.003829 255.423 <2e-16 ***
## TRTInter -0.004158 0.002444 -1.701 0.095 .
## Block2 -0.005971 0.010260 -0.582 0.563
## Block3 -0.010164 0.010768 -0.944 0.350
## Block4 -0.002088 0.002608 -0.801 0.427
## PC1 0.001497 0.001244 1.203 0.235
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.008101 on 51 degrees of freedom
## Multiple R-squared: 0.1349, Adjusted R-squared: 0.05008
## F-statistic: 1.59 on 5 and 51 DF, p-value: 0.1796## Analysis of Variance Table
##
## Response: sim
## Df Sum Sq Mean Sq F value Pr(>F)
## TRT 1 0.0001038 1.0383e-04 1.5821 0.2142
## Block 3 0.0003231 1.0771e-04 1.6412 0.1914
## PC1 1 0.0000949 9.4924e-05 1.4464 0.2347
## Residuals 51 0.0033471 6.5630e-05## Anova Table (Type II tests)
##
## Response: sim
## Sum Sq Df F value Pr(>F)
## TRT 0.0001899 1 2.8936 0.09502 .
## Block 0.0001317 3 0.6689 0.57502
## PC1 0.0000949 1 1.4464 0.23467
## Residuals 0.0033471 51
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1SimpInvPC1=lm(InvSimp~PC1+Comp+TRT+Block,RootAlphaPurp)
anova(SimpInvPC1) # Significant PC1 effect only, no Comp or Comp by PC1 effect## Analysis of Variance Table
##
## Response: InvSimp
## Df Sum Sq Mean Sq F value Pr(>F)
## PC1 1 446.3 446.32 5.4546 0.02374 *
## Comp 4 575.9 143.98 1.7596 0.15252
## Block 3 127.2 42.39 0.5181 0.67183
## Residuals 48 3927.6 81.83
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Analysis of Variance Table
##
## Response: rich
## Df Sum Sq Mean Sq F value Pr(>F)
## TRT 1 1794 1793.66 1.9903 0.16438
## Block 3 7423 2474.18 2.7454 0.05244 .
## PC1 1 1395 1395.16 1.5481 0.21910
## Residuals 51 45962 901.21
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##
## Call:
## lm(formula = rich ~ TRT + Block + PC1, data = RootAlphaPurp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -66.678 -15.781 3.311 19.513 52.108
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 467.490 14.188 32.950 <2e-16 ***
## TRTInter -17.028 9.057 -1.880 0.0658 .
## Block2 -28.723 38.021 -0.755 0.4535
## Block3 -22.647 39.902 -0.568 0.5728
## Block4 -1.931 9.663 -0.200 0.8424
## PC1 5.738 4.611 1.244 0.2191
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 30.02 on 51 degrees of freedom
## Multiple R-squared: 0.1876, Adjusted R-squared: 0.1079
## F-statistic: 2.355 on 5 and 51 DF, p-value: 0.05347## Anova Table (Type III tests)
##
## Response: sim
## Sum Sq Df F value Pr(>F)
## (Intercept) 6.6130 1 1.0031e+05 <2e-16 ***
## TRT 0.0001 1 1.7134e+00 0.1965
## Block 0.0002 3 1.0333e+00 0.3859
## PC2 0.0000 1 5.7400e-02 0.8116
## TRT:PC2 0.0000 1 4.0090e-01 0.5295
## Residuals 0.0033 50
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##
## Call:
## lm(formula = sim ~ TRT + Block + PC2, data = RootAlphaPurp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.027720 -0.004143 0.001226 0.005538 0.012149
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.722e-01 2.897e-03 335.574 <2e-16 ***
## TRTInter -2.860e-03 2.452e-03 -1.166 0.249
## Block2 5.727e-03 4.583e-03 1.250 0.217
## Block3 3.611e-03 3.187e-03 1.133 0.262
## Block4 -8.435e-05 3.198e-03 -0.026 0.979
## PC2 -8.487e-04 6.270e-04 -1.354 0.182
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.008072 on 51 degrees of freedom
## Multiple R-squared: 0.1412, Adjusted R-squared: 0.05702
## F-statistic: 1.677 on 5 and 51 DF, p-value: 0.157## Anova Table (Type III tests)
##
## Response: sim
## Sum Sq Df F value Pr(>F)
## (Intercept) 6.6130 1 1.0031e+05 <2e-16 ***
## TRT 0.0001 1 1.7134e+00 0.1965
## Block 0.0002 3 1.0333e+00 0.3859
## PC2 0.0000 1 5.7400e-02 0.8116
## TRT:PC2 0.0000 1 4.0090e-01 0.5295
## Residuals 0.0033 50
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Analysis of Variance Table
##
## Response: InvSimp
## Df Sum Sq Mean Sq F value Pr(>F)
## TRT 1 50.6 50.554 0.5864 0.4473
## Block 3 555.2 185.070 2.1468 0.1058
## PC2 1 74.7 74.736 0.8669 0.3562
## Residuals 51 4396.5 86.206## Anova Table (Type III tests)
##
## Response: InvSimp
## Sum Sq Df F value Pr(>F)
## (Intercept) 10586.5 1 121.6277 5.386e-15 ***
## TRT 90.0 1 1.0345 0.3140
## Block 405.0 3 1.5510 0.2129
## PC2 0.4 1 0.0042 0.9483
## TRT:PC2 44.5 1 0.5115 0.4778
## Residuals 4352.0 50
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1RichPC2=lm(rich~TRT+Block+PC2,RootAlphaPurp)
anova(RichPC2) # Significant coefficient SUPER small effect size## Analysis of Variance Table
##
## Response: rich
## Df Sum Sq Mean Sq F value Pr(>F)
## TRT 1 1794 1793.7 2.1642 0.14741
## Block 3 7423 2474.2 2.9853 0.03966 *
## PC2 1 5088 5087.8 6.1388 0.01658 *
## Residuals 51 42269 828.8
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1EvenPC2=lm(even~TRT+Block+PC2,RootAlphaPurp)
anova(EvenPC2) # Significant mean Evenness effect--should Check this out it is suspect## Analysis of Variance Table
##
## Response: even
## Df Sum Sq Mean Sq F value Pr(>F)
## TRT 1 1.9390e-07 1.9387e-07 1.0898 0.30145
## Block 3 1.1554e-06 3.8512e-07 2.1648 0.10354
## PC2 1 8.7980e-07 8.7979e-07 4.9454 0.03062 *
## Residuals 51 9.0729e-06 1.7790e-07
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Analysis of Variance Table
##
## Response: sim
## Df Sum Sq Mean Sq F value Pr(>F)
## TRT 1 0.0001038 1.0383e-04 1.5905 0.2130
## Block 3 0.0003231 1.0771e-04 1.6499 0.1895
## PC3 1 0.0001126 1.1260e-04 1.7247 0.1950
## Residuals 51 0.0033295 6.5283e-05## Analysis of Variance Table
##
## Response: InvSimp
## Df Sum Sq Mean Sq F value Pr(>F)
## TRT 1 50.6 50.554 0.5881 0.4467
## Block 3 555.2 185.070 2.1531 0.1050
## PC3 1 87.5 87.460 1.0175 0.3179
## Residuals 51 4383.8 85.957## Analysis of Variance Table
##
## Response: rich
## Df Sum Sq Mean Sq F value Pr(>F)
## TRT 1 1794 1793.66 1.9807 0.16538
## Block 3 7423 2474.18 2.7322 0.05325 .
## PC3 1 1173 1172.65 1.2949 0.26046
## Residuals 51 46184 905.57
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##
## Call:
## lm(formula = even ~ TRT + Block + PC3, data = RootAlphaPurp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.239e-04 -2.849e-04 -3.885e-05 2.306e-04 1.201e-03
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.035e-02 1.348e-04 76.782 <2e-16 ***
## TRTInter 1.401e-04 1.337e-04 1.047 0.3000
## Block2 -1.288e-04 2.523e-04 -0.511 0.6118
## Block3 -3.951e-04 1.658e-04 -2.383 0.0209 *
## Block4 -6.959e-05 1.394e-04 -0.499 0.6197
## PC3 -2.215e-05 4.087e-05 -0.542 0.5902
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0004405 on 51 degrees of freedom
## Multiple R-squared: 0.1244, Adjusted R-squared: 0.03858
## F-statistic: 1.449 on 5 and 51 DF, p-value: 0.2228## Analysis of Variance Table
##
## Response: even
## Df Sum Sq Mean Sq F value Pr(>F)
## TRT 1 1.9390e-07 1.9387e-07 0.9992 0.3222
## Block 3 1.1554e-06 3.8512e-07 1.9848 0.1279
## PC3 1 5.7000e-08 5.6990e-08 0.2937 0.5902
## Residuals 51 9.8957e-06 1.9403e-07### PC4
SimpPC4=lm(sim~TRT+Block+PC4,RootAlphaPurp%>%filter(sim>0.94))
summary(SimpPC4) # Significant##
## Call:
## lm(formula = sim ~ TRT + Block + PC4, data = RootAlphaPurp %>%
## filter(sim > 0.94))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.017691 -0.003427 0.001411 0.004308 0.011779
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.9744883 0.0022109 440.770 <2e-16 ***
## TRTInter -0.0025833 0.0020766 -1.244 0.219
## Block2 0.0035283 0.0041907 0.842 0.404
## Block3 0.0016194 0.0026821 0.604 0.549
## Block4 -0.0021490 0.0024082 -0.892 0.376
## PC4 0.0007738 0.0009356 0.827 0.412
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.006953 on 50 degrees of freedom
## Multiple R-squared: 0.09791, Adjusted R-squared: 0.007699
## F-statistic: 1.085 on 5 and 50 DF, p-value: 0.38## Analysis of Variance Table
##
## Response: sim
## Df Sum Sq Mean Sq F value Pr(>F)
## TRT 1 0.00005203 5.2027e-05 1.0761 0.3046
## Block 3 0.00017726 5.9087e-05 1.2222 0.3114
## PC4 1 0.00003307 3.3071e-05 0.6841 0.4121
## Residuals 50 0.00241730 4.8346e-05SimpInvPC4=lm(InvSimp~TRT+Block+PC4,RootAlphaPurp)
summary(SimpInvPC4) # Marginal InvSimp significant##
## Call:
## lm(formula = InvSimp ~ TRT + Block + PC4, data = RootAlphaPurp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.2490 -6.8413 0.7427 4.4331 25.1870
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 41.447 2.799 14.810 <2e-16 ***
## TRTInter -2.242 2.693 -0.833 0.4090
## Block2 2.810 5.370 0.523 0.6031
## Block3 2.325 3.460 0.672 0.5046
## Block4 -4.976 2.980 -1.670 0.1011
## PC4 2.083 1.054 1.977 0.0534 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.024 on 51 degrees of freedom
## Multiple R-squared: 0.182, Adjusted R-squared: 0.1018
## F-statistic: 2.27 on 5 and 51 DF, p-value: 0.06129## Analysis of Variance Table
##
## Response: InvSimp
## Df Sum Sq Mean Sq F value Pr(>F)
## TRT 1 50.6 50.55 0.6208 0.43438
## Block 3 555.2 185.07 2.2728 0.09121 .
## PC4 1 318.4 318.40 3.9102 0.05341 .
## Residuals 51 4152.9 81.43
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##
## Call:
## lm(formula = rich ~ TRT + Block + PC4, data = RootAlphaPurp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -71.495 -11.318 6.298 18.927 54.578
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 455.804 9.398 48.502 <2e-16 ***
## TRTInter -14.045 9.044 -1.553 0.1266
## Block2 9.298 18.033 0.516 0.6083
## Block3 23.133 11.620 1.991 0.0519 .
## Block4 -6.509 10.007 -0.650 0.5183
## PC4 2.686 3.538 0.759 0.4512
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 30.3 on 51 degrees of freedom
## Multiple R-squared: 0.1723, Adjusted R-squared: 0.09111
## F-statistic: 2.123 on 5 and 51 DF, p-value: 0.07759## Analysis of Variance Table
##
## Response: rich
## Df Sum Sq Mean Sq F value Pr(>F)
## TRT 1 1794 1793.66 1.9535 0.16826
## Block 3 7423 2474.18 2.6946 0.05564 .
## PC4 1 529 529.24 0.5764 0.45122
## Residuals 51 46827 918.18
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##
## Call:
## lm(formula = even ~ TRT + Block + PC4, data = RootAlphaPurp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.251e-04 -2.680e-04 -5.078e-05 2.324e-04 1.146e-03
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.037e-02 1.360e-04 76.251 <2e-16 ***
## TRTInter 1.700e-04 1.309e-04 1.299 0.1998
## Block2 -1.779e-04 2.609e-04 -0.682 0.4986
## Block3 -4.182e-04 1.681e-04 -2.487 0.0162 *
## Block4 -1.117e-04 1.448e-04 -0.772 0.4439
## PC4 4.470e-05 5.119e-05 0.873 0.3867
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0004385 on 51 degrees of freedom
## Multiple R-squared: 0.1324, Adjusted R-squared: 0.04729
## F-statistic: 1.556 on 5 and 51 DF, p-value: 0.1894## Analysis of Variance Table
##
## Response: even
## Df Sum Sq Mean Sq F value Pr(>F)
## TRT 1 1.9390e-07 1.9387e-07 1.0083 0.3201
## Block 3 1.1554e-06 3.8512e-07 2.0030 0.1252
## PC4 1 1.4660e-07 1.4660e-07 0.7624 0.3867
## Residuals 51 9.8061e-06 1.9228e-07Plotting significant linear associations
# Richness and root architecture
P2.rich=ggplot()+
geom_point(data=RootAlphaPurp,aes(PC2,rich),alpha=0.5,size=5)+
geom_smooth(data=RootAlphaPurp,method="lm",aes(PC2,rich),fullrange=TRUE)+
theme_classic()+
ylab("Richness")+
xlab("")+
Tx2
#+
#annotate("text", x = -1, y = 500, label = "paste(italic(R) ^ 2, \" = 0.15\")", parse = TRUE,hjust=0,size=5)+
# annotate("text", x = -1, y = 490, label = "paste(italic(B), \" = -4.65 +/-1.81\")", parse = TRUE,hjust=0,size=5)+
# annotate("text", x = -1, y = 480, label = "paste(italic(P), \" = 0.01\")", parse = TRUE,hjust=0,size=5)
# Evenness and root architecture
P2.even=ggplot()+
geom_point(data=RootAlphaPurp,aes(PC2,even),alpha=0.5,size=5)+
geom_smooth(data=RootAlphaPurp,method="lm",aes(PC2,even),fullrange=TRUE)+
theme_classic()+
ylab("Evenness")+
xlab("")+
Tx2#+
#annotate("text", x = -4.5, y = .0114, label = "paste(italic(R) ^ 2, \" = 0.12\")", parse = TRUE,hjust=0,size=5)+
# annotate("text", x = -4.5, y = .0112, label = "paste(italic(B), \" = -7.29E-5 +/-3.28E-5\")", parse = TRUE,hjust=0,size=5)+
# annotate("text", x = -4.5, y =.011, label = "paste(italic(P), \" = 0.04\")", parse = TRUE,hjust=0,size=5)
# Root morphology on species diversity Simpson metric
P4.Sim<-ggplot()+
geom_point(data=RootAlphaPurp,aes(PC4,sim),alpha=0.5,size=5)+
geom_smooth(data=RootAlphaPurp,method="lm",aes(PC4,sim),fullrange=TRUE)+
theme_classic()+
ylab("Simpson")+
xlab("")+
Tx2#+
#annotate("text", x = -5, y = .988, label = "paste(italic(R) ^ 2, \" = 0.18\")", parse = TRUE,hjust=0,size=5)+
#annotate("text", x = -5, y = .985, label = "paste(italic(B), \" = 2.22E-4 +/-6.99E-4\")", parse = TRUE,hjust=0,size=5)+
# annotate("text", x =-5, y = .982, label = "paste(italic(P), \" < 0.01\")", parse = TRUE,hjust=0,size=5)
P4.simIn=ggplot()+
geom_point(data=RootAlphaPurp,aes(PC4,InvSimp),alpha=0.5,size=5)+
geom_smooth(data=RootAlphaPurp,method="lm",aes(PC4,InvSimp),fullrange=TRUE)+
theme_classic()+
ylab("Inverse Simpson")+
xlab("")+
Tx2#+
# annotate("text", x = -5, y = 60, label = "paste(italic(R) ^ 2, \" = 0.12\")", parse = TRUE,hjust=0,size=5)+
# annotate("text", x = -5, y = 57, label = "paste(italic(B), \" = 2.08 +/-1.05\")", parse = TRUE,hjust=0,size=5)+
# annotate("text", x =-5, y = 54, label = "paste(italic(P), \" = 0.02\")", parse = TRUE,hjust=0,size=5)Linear mixed models
## boundary (singular) fit: see ?isSingular## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## TRT 0.00004080 4.0802e-05 1 95 0.6782 0.41228
## Block 0.00051675 1.7225e-04 3 95 2.8629 0.04084 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## sim ~ TRT + Block + (1 | ML)
## npar logLik AIC LRT Df Pr(>Chisq)
## <none> 7 318.9 -623.8
## (1 | ML) 6 318.9 -625.8 0 1 1## boundary (singular) fit: see ?isSingular## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## TRT 3 3.00 1 95 0.0349 0.852131
## Block 1064 354.66 3 95 4.1296 0.008463 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## InvSimp ~ TRT + Block + (1 | ML)
## npar logLik AIC LRT Df Pr(>Chisq)
## <none> 7 -354.24 722.48
## (1 | ML) 6 -354.24 720.48 1.1369e-13 1 1### Inverse Simpson
RichLMM=lmer(rich~TRT+Block+(1|ML),alpha%>%filter(Species=="Ip"))
anova(RichLMM)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## TRT 1254.9 1254.9 1 90.695 1.3836 0.242565
## Block 15233.7 5077.9 3 92.147 5.5989 0.001428 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## rich ~ TRT + Block + (1 | ML)
## npar logLik AIC LRT Df Pr(>Chisq)
## <none> 7 -467.16 948.32
## (1 | ML) 6 -467.29 946.58 0.26321 1 0.6079## boundary (singular) fit: see ?isSingular## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Species 0.000847 0.000847 1 167 0.1281 0.7208
## TRT 0.005399 0.005399 1 167 0.8164 0.3676
## Block 0.217604 0.072535 3 167 10.9674 1.302e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## Axis.1 ~ Species + TRT + Block + (1 | ML)
## npar logLik AIC LRT Df Pr(>Chisq)
## <none> 8 171.21 -326.41
## (1 | ML) 7 171.21 -328.41 1.7053e-13 1 1## boundary (singular) fit: see ?isSingular## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Species 0.0227878 0.0227878 1 167 4.7831 0.03013 *
## TRT 0.0000000 0.0000000 1 167 0.0000 0.99911
## Block 0.0092565 0.0030855 3 167 0.6476 0.58549
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## Axis.2 ~ Species + TRT + Block + (1 | ML)
## npar logLik AIC LRT Df Pr(>Chisq)
## <none> 8 198.59 -381.18
## (1 | ML) 7 198.59 -383.18 0 1 1## boundary (singular) fit: see ?isSingular## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Species 0.0006216 0.0006216 1 167 0.1754 0.67590
## TRT 0.0040354 0.0040354 1 167 1.1387 0.28746
## Block 0.0256465 0.0085488 3 167 2.4123 0.06861 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## Axis.3 ~ Species + TRT + Block + (1 | ML)
## npar logLik AIC LRT Df Pr(>Chisq)
## <none> 8 223.3 -430.61
## (1 | ML) 7 223.3 -432.61 0 1 1## boundary (singular) fit: see ?isSingular## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Species 0.000429 0.000429 1 167 0.2046 0.6516
## TRT 0.004337 0.004337 1 167 2.0670 0.1524
## Block 0.107444 0.035815 3 167 17.0687 1.023e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## ANOVA-like table for random-effects: Single term deletions
##
## Model:
## Axis.4 ~ Species + TRT + Block + (1 | ML)
## npar logLik AIC LRT Df Pr(>Chisq)
## <none> 8 267.06 -518.13
## (1 | ML) 7 267.06 -520.13 0 1 1Fitness=read.csv("~/Google Drive File Stream/My Drive/Field_2018/Field_2018_Rcode/CharacterDisplacementRootTraits/CleanData/FitPA4.csv")
library(dplyr)
# Calculate relative fitness
# First calculate mean seed number by species and treatment---note* we only have seed output of I. purpurea
MeanSeedNumber=aggregate(SeedNumber~Trt+Species,Fitness,mean)
colnames(MeanSeedNumber)=c("Trt","Species","MeanSeedNumber")
Ipurp.Fit=Fitness%>%
filter(Species=="Ip")
Ipurp.Alpha=alpha%>%
filter(Species=="Ip")
FitnessPurp=merge(Ipurp.Fit,MeanSeedNumber,by=c("Trt","Species"))
FitnessPurp$RelativeFit=FitnessPurp$SeedNumber/FitnessPurp$MeanSeedNumber
FitnessPurp$Block=as.factor(FitnessPurp$Block)
FitnessPurp2=merge(FitnessPurp,LeafData)
str(FitnessPurp2)## 'data.frame': 385 obs. of 24 variables:
## $ Trt : Factor w/ 2 levels "Alone","Inter": 1 1 1 1 1 1 1 1 1 1 ...
## $ Species : Factor w/ 1 level "Ip": 1 1 1 1 1 1 1 1 1 1 ...
## $ Position : Factor w/ 429 levels "102","106","107",..: 1 7 21 23 31 32 39 53 54 57 ...
## $ Block : Factor w/ 4 levels "1","2","3","4": 1 1 1 1 1 1 1 1 1 1 ...
## $ Order : int 102 114 136 138 151 153 172 203 204 213 ...
## $ ML : Factor w/ 10 levels "PA4.11Ip","PA4.13Ip",..: 10 4 10 1 3 9 4 6 6 5 ...
## $ UniqId : Factor w/ 429 levels "102Ip","106Ip",..: 1 7 21 23 31 32 39 53 54 57 ...
## $ GerminationDate: Factor w/ 5 levels "43258","43259",..: 1 1 1 1 1 1 3 3 1 1 ...
## $ Comment1 : Factor w/ 2 levels "DG","LG": NA NA NA NA NA NA NA NA NA NA ...
## $ Dead_plant : Factor w/ 1 level "Y": NA NA NA NA NA NA NA NA NA NA ...
## $ DeathCause : logi NA NA NA NA NA NA ...
## $ RootsHarvested : Factor w/ 2 levels "N","Y": 1 1 1 1 1 1 1 1 1 1 ...
## $ SeedsCounted : Factor w/ 1 level "Y": 1 1 1 1 1 1 1 1 1 1 ...
## $ Comp : Factor w/ 6 levels "PA 4.12 Ihed",..: NA NA NA NA NA NA NA NA NA NA ...
## $ Combos : Factor w/ 60 levels "PA 4.1 Ip-PA 4.12 Ihed",..: NA NA NA NA NA NA NA NA NA NA ...
## $ Population : Factor w/ 1 level "PA4": 1 1 1 1 1 1 1 1 1 1 ...
## $ SeedNumber : int 96 75 93 56 383 321 256 202 79 172 ...
## $ MeanSeedNumber : num 224 224 224 224 224 ...
## $ RelativeFit : num 0.428 0.334 0.415 0.25 1.708 ...
## $ Block.1 : int 1 1 1 1 1 1 1 1 1 1 ...
## $ Leaf.Number : int 6 5 6 7 9 10 11 7 7 8 ...
## $ Comment : logi NA NA NA NA NA NA ...
## $ X : int 1 7 21 23 31 32 39 53 54 57 ...
## $ Sample_ID : chr "102P" "114P" "136P" "138P" ...FitnessPurp2$Leaf.Number=as.numeric(as.character(FitnessPurp2$Leaf.Number))
SN1<-lmer(SeedNumber~Trt+Block+Leaf.Number+Block:Trt+(1|ML),FitnessPurp2)
anova(SN1) # Treatment is significant effect on plant seed number; Significant Treatment by Block effect## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Trt 83491 83491 1 370.05 3.9783 0.04682 *
## Block 128423 42808 3 371.69 2.0398 0.10790
## Leaf.Number 2425524 2425524 1 374.69 115.5752 < 2e-16 ***
## Trt:Block 164743 54914 3 371.54 2.6167 0.05082 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1ggplot(FitnessPurp,aes(Trt,RelativeFit,fill=Block))+
geom_boxplot()+
scale_fill_brewer("Paired")+
theme_classic()+
ylab("Relative Fitness")+
ggtitle("Relative Fitness by Treatment and Block")
# Remove size effects from fitness
StdFitness=FitnessPurp2[c("Trt","Species","Block","ML","RelativeFit","Leaf.Number")] # Subset fitness data for variables of interest
# Run one-way ANOVA to remove size effect--i.e., keep residuals
StdFitness$RelativeFitness=residuals(lm(RelativeFit~Leaf.Number,FitnessPurp2))
# Compare residuals and non-standard values of fitness
dev.off()## null device
## 1plot(StdFitness$RelativeFit,StdFitness$RelativeFitness)
# Average fitness by block, maternal line and treatment--we use NON standardized fitness (ie size effects not removed)
FitAveraged=aggregate(RelativeFit~Block+Trt+ML,FitnessPurp,mean)
colnames(FitAveraged)<-c("Block","Trt","ML","RelativeFitness")
FitAveraged$TRT=FitAveraged$Trt
dim(FitAveraged)## [1] 76 5## Block Trt ML RelativeFitness TRT
## 1 1 Alone PA4.11Ip 0.4437172 Alone
## 2 2 Alone PA4.11Ip 1.0435158 Alone
## 3 3 Alone PA4.11Ip 1.0747321 Alone
## 4 4 Alone PA4.11Ip 1.4627059 Alone
## 5 1 Inter PA4.11Ip 0.6619616 Inter
## 6 2 Inter PA4.11Ip 0.6103389 Inter# Average size
SizeAveraged=aggregate(Leaf.Number~Block+Trt+ML+Species,LeafData,mean)
colnames(SizeAveraged)<-c("Block","Trt","ML","Species","Size")
SizeAveraged$TRT=SizeAveraged$Trt
dim(SizeAveraged)## [1] 76 6## Block Trt ML Species Size TRT
## 1 1 Alone PA4.11Ip Ip 9.000000 Alone
## 2 2 Alone PA4.11Ip Ip 11.000000 Alone
## 3 3 Alone PA4.11Ip Ip 8.000000 Alone
## 4 4 Alone PA4.11Ip Ip 5.000000 Alone
## 5 1 Inter PA4.11Ip Ip 7.545455 Inter
## 6 2 Inter PA4.11Ip Ip 7.500000 Inter#### #### #### #### #### #### ####
# Examine selection on microbiome first
#### #### #### #### #### #### ####
FitnessPurp$TRT=FitnessPurp$Trt
FitnessPurp$Combos=as.character(FitnessPurp$Combos)
FitnessPurp[which(FitnessPurp$Trt=="Alone"),]$Combos="none"
FitnessPurp$Combos=as.factor(FitnessPurp$Combos)
BrayFit=merge(physeq.pcoa.df,FitAveraged)
FitAlpha=merge(FitAveraged,alpha)
dim(FitAlpha)## [1] 97 13ggplot(FitAlpha,aes(TRT,RelativeFitness))+
geom_boxplot()+
scale_fill_brewer("Paired")+
theme_classic()+
ylab("Relative Fitness")+
ggtitle("Relative Fitness by Treatment and Block")+
facet_grid(~Block)
# Combine with root data
library(dplyr)
RootAveraged=aggregate(list(RootData[c("PC1","PC2","PC3","PC4")]),by=list(RootData$Trt,RootData$ML),FUN=mean)
colnames(RootAveraged)=c("Trt","ML","PC1","PC2","PC3","PC4")
head(RootAveraged)## Trt ML PC1 PC2 PC3 PC4
## 1 Alone PA4.11Ip -0.69794646 -1.3274069 0.7756816 -0.75520608
## 2 Inter PA4.11Ip 0.43519578 0.6954043 -0.1859846 0.10761866
## 3 Inter PA4.12Ihed 0.07075942 -0.9146971 -0.2814713 -0.01631047
## 4 Alone PA4.13Ip -2.28254650 1.4831488 0.9299528 -0.64140759
## 5 Inter PA4.13Ip 0.11317327 -0.1860671 0.1006711 0.43992946
## 6 Alone PA4.14Ip 0.70071833 -0.4492977 0.9728631 -0.41237743## ML Trt Block TRT RelativeFitness Sample_ID Species
## 1 PA4.11Ip Alone 1 Alone 0.4437172 158P Ip
## 2 PA4.11Ip Alone 1 Alone 0.4437172 84P Ip
## 3 PA4.11Ip Alone 4 Alone 1.4627059 814P Ip
## 4 PA4.11Ip Alone 3 Alone 1.0747321 674P Ip
## 5 PA4.11Ip Inter 1 Inter 0.6619616 93AP Ip
## 6 PA4.11Ip Inter 1 Inter 0.6619616 21P Ip
## Combos rich InvSimp sim shan even
## 1 none 443 31.85241 0.9686052 4.536983 0.01024150
## 2 none 469 40.47708 0.9752947 4.739450 0.01010544
## 3 none 471 49.18046 0.9796667 4.800749 0.01019267
## 4 none 443 30.20342 0.9668912 4.479767 0.01011234
## 5 PA 4.11 Ip-PA 4.15 Ihed 432 34.99536 0.9714248 4.587454 0.01061911
## 6 PA 4.11 Ip-PA 4.3 Ihed 486 41.55300 0.9759344 4.745673 0.00976476
## PC1 PC2 PC3 PC4
## 1 -0.6979465 -1.3274069 0.7756816 -0.7552061
## 2 -0.6979465 -1.3274069 0.7756816 -0.7552061
## 3 -0.6979465 -1.3274069 0.7756816 -0.7552061
## 4 -0.6979465 -1.3274069 0.7756816 -0.7552061
## 5 0.4351958 0.6954043 -0.1859846 0.1076187
## 6 0.4351958 0.6954043 -0.1859846 0.1076187#RootFitLeafAlpha=merge(RootFitAlpha,LeafData[c("Sample_ID","Leaf.Number")],by="Sample_ID")
#RootFitLeafAlpha$Leaf.Number=as.numeric(as.character(RootFitLeafAlpha$Leaf.Number))
# CombinE root,fitness/bray estimates
RootFitBray=merge(BrayFit,RootAveraged)
# Plot boxplots of averaged root traits
PC2_Box=ggplot(RootAveraged,aes(x="",y=PC2))+
geom_boxplot()+
#geom_jitter()+
xlab("Root Architecture")+
theme_classic()+
Tx+
coord_flip()
# Plot boxplots of averaged root traits
PC1_Box=ggplot(RootAveraged,aes(x="",y=PC1))+
geom_boxplot()+
#geom_jitter()+
xlab("Root Topology")+
theme_classic()+
Tx+
coord_flip()
# Plot boxplots of averaged root traits
PC4_Box=ggplot(RootAveraged,aes(x="",y=PC4))+
geom_boxplot()+
#geom_jitter()+
xlab("Root Morphology")+
theme_classic()+
Tx+
coord_flip()
#ggarrange(P2.rich,P2.even,P4.Sim,P4.simIn,nrow=2,ncol=2)
AB=cowplot::plot_grid(P2.rich,P2.even,align = "hv", ncol = 2,labels =c("A","B"), label_size =22 ,hjust=-11,vjust=1,label_x = -0.16)## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'ab=cowplot::plot_grid(P4.Sim,P4.simIn,align = "hv", ncol = 2,labels =c("A","B"), label_size =22 ,hjust=-11,vjust=1,label_x = -0.17)## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'## `geom_smooth()` using formula 'y ~ x'
# Common x title
x.grob <- textGrob("Root morphology (PC4)",
gp=gpar(col="black", fontsize=25), rot=0)
gridExtra::grid.arrange(gridExtra::arrangeGrob(ab,bottom=x.grob,padding = unit(0.5,units = 'in'),nrow=1))
# Common x title
x.grob1 <- textGrob("Root architecture (PC2)",
gp=gpar(col="black", fontsize=25), rot=0)
gridExtra::grid.arrange(gridExtra::arrangeGrob(AB,bottom=x.grob1,padding = unit(0.5,units = 'in'),nrow=1))
Selection on microbe variables
# Quadratic microbe term
FitAlpha$even2=(FitAlpha$even*FitAlpha$even)
FitAlpha$rich2=(FitAlpha$rich*FitAlpha$rich)
FitAlpha$InSim2=(FitAlpha$InvSimp*FitAlpha$InvSimp)
FitAlpha$sim2=(FitAlpha$sim*FitAlpha$sim)Selection on richness
##
## Call:
## lm(formula = RelativeFitness ~ Block + rich + rich2, data = FitAlpha %>%
## filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.79140 -0.16551 0.00835 0.14613 0.98238
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.225e-01 1.561e+01 -0.027 0.9787
## Block2 2.227e-01 2.768e-01 0.804 0.4316
## Block3 5.423e-01 3.247e-01 1.670 0.1123
## Block4 6.396e-01 2.571e-01 2.488 0.0229 *
## rich 9.591e-04 6.938e-02 0.014 0.9891
## rich2 2.624e-06 7.721e-05 0.034 0.9733
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4427 on 18 degrees of freedom
## Multiple R-squared: 0.3552, Adjusted R-squared: 0.1761
## F-statistic: 1.983 on 5 and 18 DF, p-value: 0.1301##
## Call:
## lm(formula = RelativeFitness ~ Block + rich + rich2, data = FitAlpha %>%
## filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.40909 -0.10830 -0.01740 0.06575 0.68679
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.563e+00 3.295e+00 -1.385 0.171
## Block2 6.645e-02 6.771e-02 0.981 0.330
## Block3 7.799e-01 6.929e-02 11.256 < 2e-16 ***
## Block4 3.027e-01 7.006e-02 4.320 5.29e-05 ***
## rich 2.474e-02 1.516e-02 1.633 0.107
## rich2 -2.891e-05 1.735e-05 -1.666 0.100
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2001 on 67 degrees of freedom
## Multiple R-squared: 0.717, Adjusted R-squared: 0.6959
## F-statistic: 33.95 on 5 and 67 DF, p-value: < 2.2e-16richness_sel=lm(RelativeFitness~TRT*Block+rich,FitAlpha)
summary(richness_sel) # No evidence of indirect selection##
## Call:
## lm(formula = RelativeFitness ~ TRT * Block + rich, data = FitAlpha)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.71196 -0.12913 -0.03669 0.10339 0.98681
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.4565102 0.4562438 1.001 0.319771
## TRTInter 0.1178495 0.1305712 0.903 0.369219
## Block2 0.1530488 0.1585365 0.965 0.336998
## Block3 0.6301298 0.1666124 3.782 0.000283 ***
## Block4 0.5881335 0.1521200 3.866 0.000211 ***
## rich 0.0002558 0.0009621 0.266 0.790984
## TRTInter:Block2 -0.0670337 0.1824968 -0.367 0.714267
## TRTInter:Block3 0.1244367 0.1874137 0.664 0.508447
## TRTInter:Block4 -0.2594529 0.1780784 -1.457 0.148687
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2718 on 88 degrees of freedom
## Multiple R-squared: 0.5685, Adjusted R-squared: 0.5292
## F-statistic: 14.49 on 8 and 88 DF, p-value: 2.733e-13## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## TRT 1 0.1156 0.11565 1.5656 0.2142
## Block 3 8.0999 2.69998 36.5513 1.955e-15 ***
## rich 1 0.0006 0.00059 0.0079 0.9292
## TRT:Block 3 0.3471 0.11570 1.5664 0.2032
## Residuals 88 6.5004 0.07387
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1ggplot(FitAlpha)+
geom_point(aes(RelativeFitness,rich),alpha=0.5,size=5)+
geom_smooth(method="lm",aes(RelativeFitness,rich),fullrange=TRUE)+
theme_classic()+
ylab("Relative fitness")+
xlab("Richness")+
Tx2## `geom_smooth()` using formula 'y ~ x'
Selection on Inverse Simpson
##
## Call:
## lm(formula = RelativeFitness ~ Block + InvSimp + InSim2, data = FitAlpha %>%
## filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.72828 -0.16024 -0.05544 0.15054 0.99454
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.8744784 2.3659317 0.370 0.7160
## Block2 0.1476774 0.2696585 0.548 0.5907
## Block3 0.6139853 0.2879193 2.132 0.0470 *
## Block4 0.5781498 0.2650997 2.181 0.0427 *
## InvSimp -0.0194253 0.1231302 -0.158 0.8764
## InSim2 0.0002973 0.0016102 0.185 0.8556
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4522 on 18 degrees of freedom
## Multiple R-squared: 0.3274, Adjusted R-squared: 0.1406
## F-statistic: 1.753 on 5 and 18 DF, p-value: 0.1737##
## Call:
## lm(formula = RelativeFitness ~ Block + InvSimp + InSim2, data = FitAlpha %>%
## filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.39125 -0.10854 -0.02030 0.06625 0.71852
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.830e-01 2.687e-01 3.286 0.00162 **
## Block2 9.491e-02 6.865e-02 1.382 0.17142
## Block3 7.748e-01 7.062e-02 10.970 < 2e-16 ***
## Block4 3.221e-01 7.008e-02 4.596 1.96e-05 ***
## InvSimp -8.561e-03 1.356e-02 -0.632 0.52985
## InSim2 8.071e-05 1.665e-04 0.485 0.62936
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2033 on 67 degrees of freedom
## Multiple R-squared: 0.7078, Adjusted R-squared: 0.686
## F-statistic: 32.46 on 5 and 67 DF, p-value: < 2.2e-16Invn_sel=lm(RelativeFitness~TRT*Block+InvSimp+Block,FitAlpha)
summary(Invn_sel) # No evidence of indirect selection##
## Call:
## lm(formula = RelativeFitness ~ TRT * Block + InvSimp + Block,
## data = FitAlpha)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.70581 -0.14022 -0.02634 0.10538 0.98955
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.627240 0.164324 3.817 0.000251 ***
## TRTInter 0.108641 0.129286 0.840 0.403010
## Block2 0.142704 0.157121 0.908 0.366229
## Block3 0.640412 0.164643 3.890 0.000195 ***
## Block4 0.580133 0.151326 3.834 0.000237 ***
## InvSimp -0.001360 0.003106 -0.438 0.662675
## TRTInter:Block2 -0.053652 0.182000 -0.295 0.768848
## TRTInter:Block3 0.132110 0.188137 0.702 0.484407
## TRTInter:Block4 -0.256351 0.177514 -1.444 0.152258
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2716 on 88 degrees of freedom
## Multiple R-squared: 0.5691, Adjusted R-squared: 0.5299
## F-statistic: 14.53 on 8 and 88 DF, p-value: 2.58e-13ggplot(FitAlpha)+
geom_point(aes(RelativeFitness,InvSimp),alpha=0.5,size=5)+
geom_smooth(method="lm",aes(RelativeFitness,InvSimp),fullrange=TRUE)+
theme_classic()+
ylab("Relative fitness")+
xlab("Inverse Simpson")+
Tx2## `geom_smooth()` using formula 'y ~ x'
Selection on Simpson
##
## Call:
## lm(formula = RelativeFitness ~ Block + sim + sim2, data = FitAlpha %>%
## filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.73020 -0.15925 -0.01442 0.14021 0.98152
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 113.7563 2548.9022 0.045 0.9649
## Block2 0.1563 0.2691 0.581 0.5685
## Block3 0.6308 0.2812 2.243 0.0377 *
## Block4 0.5915 0.2627 2.252 0.0371 *
## sim -236.8309 5252.7315 -0.045 0.9645
## sim2 123.8459 2706.1541 0.046 0.9640
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4527 on 18 degrees of freedom
## Multiple R-squared: 0.3257, Adjusted R-squared: 0.1385
## F-statistic: 1.739 on 5 and 18 DF, p-value: 0.1767##
## Call:
## lm(formula = RelativeFitness ~ Block + sim + sim2, data = FitAlpha %>%
## filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.39853 -0.12744 -0.02723 0.06812 0.69878
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -161.47060 174.42097 -0.926 0.358
## Block2 0.08882 0.06838 1.299 0.198
## Block3 0.78244 0.06950 11.259 < 2e-16 ***
## Block4 0.31980 0.06979 4.582 2.06e-05 ***
## sim 338.30099 361.47826 0.936 0.353
## sim2 -176.40402 187.27506 -0.942 0.350
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2025 on 67 degrees of freedom
## Multiple R-squared: 0.71, Adjusted R-squared: 0.6883
## F-statistic: 32.81 on 5 and 67 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = RelativeFitness ~ TRT * Block + sim, data = FitAlpha)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.70371 -0.13867 -0.02266 0.09800 0.98995
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.03554 3.58756 0.567 0.571895
## TRTInter 0.10621 0.12993 0.817 0.415883
## Block2 0.14248 0.15723 0.906 0.367316
## Block3 0.63853 0.16453 3.881 0.000201 ***
## Block4 0.57937 0.15150 3.824 0.000245 ***
## sim -1.50026 3.68123 -0.408 0.684600
## TRTInter:Block2 -0.05202 0.18262 -0.285 0.776440
## TRTInter:Block3 0.13144 0.18813 0.699 0.486619
## TRTInter:Block4 -0.25457 0.17758 -1.434 0.155238
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2716 on 88 degrees of freedom
## Multiple R-squared: 0.5689, Adjusted R-squared: 0.5298
## F-statistic: 14.52 on 8 and 88 DF, p-value: 2.612e-13ggplot(FitAlpha)+
geom_point(aes(RelativeFitness,sim),alpha=0.5,size=5)+
geom_smooth(method="lm",aes(RelativeFitness,sim),fullrange=TRUE)+
theme_classic()+
ylab("Relative fitness")+
xlab("Simpson")+
Tx2## `geom_smooth()` using formula 'y ~ x'
Selection on Evenness
##
## Call:
## lm(formula = RelativeFitness ~ Block + even + even2, data = FitAlpha %>%
## filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.82007 -0.15847 0.00148 0.13980 0.99277
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.344e+00 3.941e+01 -0.085 0.9333
## Block2 2.484e-01 2.763e-01 0.899 0.3805
## Block3 5.492e-01 3.258e-01 1.685 0.1092
## Block4 6.486e-01 2.550e-01 2.544 0.0204 *
## even 1.011e+03 7.594e+03 0.133 0.8955
## even2 -6.154e+04 3.661e+05 -0.168 0.8684
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4398 on 18 degrees of freedom
## Multiple R-squared: 0.3637, Adjusted R-squared: 0.187
## F-statistic: 2.058 on 5 and 18 DF, p-value: 0.1186summary(lm(RelativeFitness~Block+even+even2,FitAlpha%>%filter(TRT!="Alone"))) # Significant quadratic term for evenness on fitnes (super low slope tho)##
## Call:
## lm(formula = RelativeFitness ~ Block + even + even2, data = FitAlpha %>%
## filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.43781 -0.11504 -0.03577 0.08246 0.68928
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.991e+01 8.357e+00 -2.382 0.0200 *
## Block2 9.363e-02 6.588e-02 1.421 0.1598
## Block3 7.744e-01 6.681e-02 11.590 < 2e-16 ***
## Block4 3.112e-01 6.761e-02 4.602 1.92e-05 ***
## even 3.920e+03 1.591e+03 2.464 0.0163 *
## even2 -1.862e+05 7.566e+04 -2.461 0.0164 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.196 on 67 degrees of freedom
## Multiple R-squared: 0.7284, Adjusted R-squared: 0.7081
## F-statistic: 35.93 on 5 and 67 DF, p-value: < 2.2e-16even_sel=lm(RelativeFitness~Trt*Block+TRT*even2+even,FitAlpha) # if we include block by treatment interaction there is marginal significance for a treatment by evenness squared effect
even_sel2=lm(RelativeFitness~Block+TRT*even2+even,FitAlpha) # if we include block by treatment interaction there is marginal significance for a treatment by evenness squared effect
anova(even_sel,even_sel2) # Based on RSS--second model/simpler one is a bit better## Analysis of Variance Table
##
## Model 1: RelativeFitness ~ Trt * Block + TRT * even2 + even
## Model 2: RelativeFitness ~ Block + TRT * even2 + even
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 86 6.079
## 2 89 6.596 -3 -0.51695 2.4378 0.07003 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## Trt 1 0.1156 0.11565 1.6361 0.20430
## Block 3 8.0999 2.69998 38.1967 8.693e-16 ***
## even2 1 0.0103 0.01034 0.1463 0.70302
## even 1 0.1970 0.19695 2.7863 0.09871 .
## Trt:Block 3 0.3230 0.10767 1.5232 0.21426
## TRT:even2 1 0.2388 0.23877 3.3779 0.06953 .
## Residuals 86 6.0790 0.07069
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1ggplot(FitAlpha)+
geom_point(aes(RelativeFitness,even),alpha=0.5,size=5)+
stat_smooth(method="lm",formula = y ~poly(x,2),aes(RelativeFitness,even))+
theme_classic()+
ylab("Relative fitness")+
xlab("Evenness")+
Tx2
# Remove block effects from fitness
RootFitAlpha$FitResidBlk<-resid(lm(RelativeFitness~Block,RootFitAlpha))
RootFitAlpha$Comp<-sub(".*\\-","",RootFitAlpha$Combos)
# PC1 and richness
richPC1=lm(RelativeFitness~PC1*rich*Trt*Block-PC1:rich:Trt:Block,RootFitAlpha)
#summary(richPC1)
anova(richPC1)## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## PC1 1 0.1572 0.15720 2.6474 0.1083472
## rich 1 0.7744 0.77437 13.0411 0.0005784 ***
## Trt 1 0.1057 0.10568 1.7797 0.1866326
## Block 3 7.2159 2.40529 40.5074 3.933e-15 ***
## PC1:rich 1 0.0000 0.00002 0.0004 0.9848097
## PC1:Trt 1 0.0086 0.00860 0.1448 0.7047266
## rich:Trt 1 0.0105 0.01046 0.1762 0.6759774
## PC1:Block 3 0.5911 0.19704 3.3183 0.0248966 *
## rich:Block 3 0.2154 0.07180 1.2091 0.3131001
## Trt:Block 3 0.1673 0.05578 0.9393 0.4265873
## PC1:rich:Trt 1 0.0721 0.07211 1.2145 0.2743372
## PC1:rich:Block 3 0.6228 0.20759 3.4960 0.0201213 *
## PC1:Trt:Block 3 0.9197 0.30657 5.1629 0.0028326 **
## rich:Trt:Block 3 0.1653 0.05510 0.9279 0.4321120
## Residuals 68 4.0378 0.05938
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Within treatment w block removed
summary(lm(FitResidBlk~rich+PC1,RootFitAlpha%>%filter(TRT=="Alone")))##
## Call:
## lm(formula = FitResidBlk ~ rich + PC1, data = RootFitAlpha %>%
## filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.78070 -0.20666 0.02256 0.14172 0.88602
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.2122161 1.2912061 -0.164 0.871
## rich 0.0004741 0.0028073 0.169 0.868
## PC1 0.0321677 0.0728484 0.442 0.663
##
## Residual standard error: 0.4319 on 21 degrees of freedom
## Multiple R-squared: 0.01116, Adjusted R-squared: -0.08302
## F-statistic: 0.1185 on 2 and 21 DF, p-value: 0.8889##
## Call:
## lm(formula = FitResidBlk ~ rich + PC1, data = RootFitAlpha %>%
## filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.43010 -0.09771 -0.03501 0.08772 0.75569
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0992588 0.3370733 0.294 0.769
## rich -0.0001961 0.0007567 -0.259 0.796
## PC1 0.0145365 0.0324388 0.448 0.655
##
## Residual standard error: 0.2027 on 70 degrees of freedom
## Multiple R-squared: 0.003209, Adjusted R-squared: -0.02527
## F-statistic: 0.1127 on 2 and 70 DF, p-value: 0.8936##
## Call:
## lm(formula = RelativeFitness ~ PC2 * rich * Block, data = RootFitAlpha %>%
## filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.75212 -0.06477 0.02312 0.11124 0.75503
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.491e-01 1.170e+01 0.073 0.944
## PC2 4.371e-01 9.655e+00 0.045 0.965
## rich -5.203e-04 2.522e-02 -0.021 0.984
## Block2 2.727e-01 1.236e+01 0.022 0.983
## Block3 1.391e+01 1.515e+01 0.919 0.385
## Block4 -1.308e+00 1.217e+01 -0.107 0.917
## PC2:rich -8.395e-04 2.093e-02 -0.040 0.969
## PC2:Block2 1.332e+00 1.051e+01 0.127 0.902
## PC2:Block3 3.069e+01 1.921e+01 1.598 0.149
## PC2:Block4 1.955e-02 1.056e+01 0.002 0.999
## rich:Block2 -8.649e-05 2.671e-02 -0.003 0.997
## rich:Block3 -2.777e-02 3.209e-02 -0.865 0.412
## rich:Block4 3.858e-03 2.639e-02 0.146 0.887
## PC2:rich:Block2 -3.053e-03 2.296e-02 -0.133 0.898
## PC2:rich:Block3 -6.754e-02 4.164e-02 -1.622 0.143
## PC2:rich:Block4 -6.021e-04 2.326e-02 -0.026 0.980
##
## Residual standard error: 0.4923 on 8 degrees of freedom
## Multiple R-squared: 0.6457, Adjusted R-squared: -0.01864
## F-statistic: 0.9719 on 15 and 8 DF, p-value: 0.5432##
## Call:
## lm(formula = RelativeFitness ~ PC2 * rich * Block, data = RootFitAlpha %>%
## filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.45821 -0.07770 -0.02237 0.08282 0.56703
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.152e+00 5.414e-01 2.128 0.0377 *
## PC2 -2.461e-02 8.424e-01 -0.029 0.9768
## rich -1.050e-03 1.228e-03 -0.855 0.3959
## Block2 -4.257e-01 9.710e-01 -0.438 0.6627
## Block3 1.298e+00 9.152e-01 1.418 0.1616
## Block4 -1.991e+00 1.226e+00 -1.624 0.1100
## PC2:rich -2.843e-05 1.928e-03 -0.015 0.9883
## PC2:Block2 2.477e-01 1.588e+00 0.156 0.8766
## PC2:Block3 3.295e+00 2.090e+00 1.577 0.1203
## PC2:Block4 8.472e-01 2.494e+00 0.340 0.7353
## rich:Block2 1.163e-03 2.194e-03 0.530 0.5980
## rich:Block3 -1.101e-03 2.007e-03 -0.548 0.5856
## rich:Block4 5.300e-03 2.771e-03 1.912 0.0609 .
## PC2:rich:Block2 -8.457e-04 3.570e-03 -0.237 0.8136
## PC2:rich:Block3 -6.687e-03 4.469e-03 -1.496 0.1401
## PC2:rich:Block4 -1.126e-03 5.618e-03 -0.200 0.8419
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1882 on 57 degrees of freedom
## Multiple R-squared: 0.7871, Adjusted R-squared: 0.731
## F-statistic: 14.04 on 15 and 57 DF, p-value: 5.429e-14## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## PC2 1 0.0335 0.03349 0.5013 0.4813678
## rich 1 0.8044 0.80440 12.0392 0.0009089 ***
## Trt 1 0.2590 0.25904 3.8770 0.0530293 .
## Block 3 7.1307 2.37690 35.5745 6.098e-14 ***
## PC2:rich 1 0.0025 0.00249 0.0372 0.8476339
## PC2:Trt 1 0.0432 0.04323 0.6469 0.4240096
## rich:Trt 1 0.0136 0.01364 0.2042 0.6528072
## PC2:Block 3 0.0946 0.03153 0.4720 0.7028213
## rich:Block 3 0.2088 0.06959 1.0415 0.3798857
## Trt:Block 3 0.3429 0.11429 1.7106 0.1730218
## PC2:rich:Trt 1 0.0095 0.00949 0.1421 0.7073849
## PC2:rich:Block 3 0.3372 0.11239 1.6822 0.1790121
## PC2:Trt:Block 3 1.2357 0.41189 6.1646 0.0009058 ***
## rich:Trt:Block 3 0.0047 0.00157 0.0235 0.9950628
## Residuals 68 4.5434 0.06681
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Phenotypic selection on root architecture according to block and treatment--significant interaction between PC2, richness, treatment and block
# PC3 and richness
summary(lm(RelativeFitness~Block*PC3*rich,RootFitAlpha%>%filter(TRT=="Alone")))##
## Call:
## lm(formula = RelativeFitness ~ Block * PC3 * rich, data = RootFitAlpha %>%
## filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.43811 -0.10466 0.00042 0.07339 0.88436
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -10.52245 34.19258 -0.308 0.766
## Block2 10.98549 34.38835 0.319 0.758
## Block3 24.40983 41.53757 0.588 0.573
## Block4 20.09306 35.66792 0.563 0.589
## PC3 12.68878 41.58761 0.305 0.768
## rich 0.02341 0.07206 0.325 0.754
## Block2:PC3 -14.25921 41.80697 -0.341 0.742
## Block3:PC3 -33.04273 51.00990 -0.648 0.535
## Block4:PC3 -20.59474 43.06326 -0.478 0.645
## Block2:rich -0.02266 0.07254 -0.312 0.763
## Block3:rich -0.04798 0.08519 -0.563 0.589
## Block4:rich -0.03986 0.07523 -0.530 0.611
## PC3:rich -0.02684 0.08812 -0.305 0.768
## Block2:PC3:rich 0.03013 0.08866 0.340 0.743
## Block3:PC3:rich 0.06729 0.10518 0.640 0.540
## Block4:PC3:rich 0.04133 0.09128 0.453 0.663
##
## Residual standard error: 0.4835 on 8 degrees of freedom
## Multiple R-squared: 0.6583, Adjusted R-squared: 0.0175
## F-statistic: 1.027 on 15 and 8 DF, p-value: 0.5084##
## Call:
## lm(formula = RelativeFitness ~ Block * PC3 * rich, data = RootFitAlpha %>%
## filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.39876 -0.08191 -0.02446 0.06407 0.48998
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.0452625 0.6052994 1.727 0.0896 .
## Block2 -0.8173359 0.9280059 -0.881 0.3822
## Block3 2.3109108 1.1116370 2.079 0.0421 *
## Block4 -0.3914877 1.0899094 -0.359 0.7208
## PC3 0.0590131 1.7451974 0.034 0.9731
## rich -0.0008076 0.0013886 -0.582 0.5631
## Block2:PC3 -0.0830240 2.2172878 -0.037 0.9703
## Block3:PC3 -7.9595873 4.1043488 -1.939 0.0574 .
## Block4:PC3 -1.0978146 3.0536554 -0.360 0.7205
## Block2:rich 0.0019886 0.0021187 0.939 0.3519
## Block3:rich -0.0031651 0.0024337 -1.301 0.1987
## Block4:rich 0.0016710 0.0025123 0.665 0.5087
## PC3:rich -0.0003039 0.0042277 -0.072 0.9429
## Block2:PC3:rich 0.0008147 0.0052460 0.155 0.8771
## Block3:PC3:rich 0.0161945 0.0088796 1.824 0.0734 .
## Block4:PC3:rich 0.0023786 0.0071130 0.334 0.7393
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1938 on 57 degrees of freedom
## Multiple R-squared: 0.7742, Adjusted R-squared: 0.7147
## F-statistic: 13.03 on 15 and 57 DF, p-value: 2.615e-13richPC3=lm(RelativeFitness~PC3*rich*Trt*Block-PC3:rich:Trt:Block,RootFitAlpha)
anova(richPC3) # Significant richness effect## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## PC3 1 0.1472 0.14717 2.4483 0.1222966
## rich 1 0.9017 0.90166 14.9998 0.0002441 ***
## Trt 1 0.0665 0.06651 1.1064 0.2965797
## Block 3 7.3184 2.43947 40.5825 3.779e-15 ***
## PC3:rich 1 0.0156 0.01558 0.2591 0.6123829
## PC3:Trt 1 0.0898 0.08983 1.4944 0.2257586
## rich:Trt 1 0.0097 0.00970 0.1614 0.6891054
## PC3:Block 3 0.3439 0.11463 1.9070 0.1366853
## rich:Block 3 0.1886 0.06285 1.0456 0.3781295
## Trt:Block 3 0.5922 0.19741 3.2840 0.0259439 *
## PC3:rich:Trt 1 0.2373 0.23729 3.9475 0.0509707 .
## PC3:rich:Block 3 0.5972 0.19906 3.3115 0.0251024 *
## PC3:Trt:Block 3 0.3319 0.11065 1.8407 0.1480213
## rich:Trt:Block 3 0.1362 0.04539 0.7550 0.5232594
## Residuals 68 4.0876 0.06011
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##
## Call:
## lm(formula = RelativeFitness ~ PC3 * rich * Trt * Block - PC3:rich:Trt:Block,
## data = RootFitAlpha)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.54717 -0.09467 0.00121 0.06952 0.86706
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.7934288 6.0893893 0.130 0.8967
## PC3 -1.7912322 3.6311645 -0.493 0.6234
## rich -0.0004125 0.0129428 -0.032 0.9747
## TrtInter 0.2394549 6.0901832 0.039 0.9688
## Block2 -0.0678830 6.0838280 -0.011 0.9911
## Block3 5.8685034 7.2257215 0.812 0.4195
## Block4 6.4827149 6.5202879 0.994 0.3236
## PC3:rich 0.0038413 0.0076766 0.500 0.6184
## PC3:TrtInter 2.0310950 2.6859550 0.756 0.4521
## rich:TrtInter -0.0003614 0.0129342 -0.028 0.9778
## PC3:Block2 -0.2626247 3.0679137 -0.086 0.9320
## PC3:Block3 -9.3501717 5.4372185 -1.720 0.0900 .
## PC3:Block4 -3.4154144 3.9150703 -0.872 0.3861
## rich:Block2 0.0005663 0.0129780 0.044 0.9653
## rich:Block3 -0.0102484 0.0148849 -0.689 0.4935
## rich:Block4 -0.0111626 0.0138772 -0.804 0.4240
## TrtInter:Block2 -0.7474835 6.1371196 -0.122 0.9034
## TrtInter:Block3 -3.3957436 6.9593233 -0.488 0.6272
## TrtInter:Block4 -6.7298917 6.4612809 -1.042 0.3013
## PC3:rich:TrtInter -0.0045850 0.0056217 -0.816 0.4176
## PC3:rich:Block2 0.0005564 0.0064865 0.086 0.9319
## PC3:rich:Block3 0.0186962 0.0107710 1.736 0.0871 .
## PC3:rich:Block4 0.0048847 0.0082915 0.589 0.5577
## PC3:TrtInter:Block2 0.3051472 0.5331783 0.572 0.5690
## PC3:TrtInter:Block3 0.2294980 0.6945541 0.330 0.7421
## PC3:TrtInter:Block4 1.2326639 0.5739178 2.148 0.0353 *
## rich:TrtInter:Block2 0.0014111 0.0131000 0.108 0.9145
## rich:TrtInter:Block3 0.0067307 0.0143649 0.469 0.6409
## rich:TrtInter:Block4 0.0124899 0.0137449 0.909 0.3667
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2452 on 68 degrees of freedom
## Multiple R-squared: 0.7286, Adjusted R-squared: 0.6169
## F-statistic: 6.521 on 28 and 68 DF, p-value: 1.461e-10# With block removed
Model1a<-(lm(RelativeFitness~rich+PC3,RootFitAlpha%>%filter(TRT=="Alone")))
Model1c<-(lm(RelativeFitness~rich+PC3,RootFitAlpha%>%filter(TRT!="Alone"))) # Richness is significant when Block is not in the model, and marginal with the interaction
summary(Model1a)##
## Call:
## lm(formula = RelativeFitness ~ rich + PC3, data = RootFitAlpha %>%
## filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.5014 -0.3234 -0.2056 0.2228 1.2122
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.513143 1.508149 -0.340 0.737
## rich 0.003321 0.003240 1.025 0.317
## PC3 -0.127941 0.200651 -0.638 0.531
##
## Residual standard error: 0.49 on 21 degrees of freedom
## Multiple R-squared: 0.07855, Adjusted R-squared: -0.009212
## F-statistic: 0.895 on 2 and 21 DF, p-value: 0.4236##
## Call:
## lm(formula = RelativeFitness ~ rich + PC3, data = RootFitAlpha %>%
## filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.56635 -0.30499 -0.00652 0.22647 1.10383
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.276641 0.580838 -0.476 0.6354
## rich 0.002862 0.001305 2.192 0.0317 *
## PC3 -0.032345 0.116139 -0.279 0.7814
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3559 on 70 degrees of freedom
## Multiple R-squared: 0.06429, Adjusted R-squared: 0.03756
## F-statistic: 2.405 on 2 and 70 DF, p-value: 0.0977# Significant Block effects
# PC3:rich:Block Significant
# TRT:Block significant
# PC3:rich:TRT significant
# PC4 and richness
richPC4=lm(RelativeFitness~PC4*rich*Trt*Block-PC4:rich:Trt:Block,RootFitAlpha)
anova(richPC4)## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## PC4 1 0.3109 0.31087 4.6331 0.034913 *
## rich 1 0.6603 0.66034 9.8413 0.002522 **
## Trt 1 0.1668 0.16681 2.4860 0.119507
## Block 3 7.0800 2.36001 35.1722 7.702e-14 ***
## PC4:rich 1 0.0934 0.09341 1.3921 0.242158
## PC4:Trt 1 0.0019 0.00195 0.0291 0.865166
## rich:Trt 1 0.0491 0.04909 0.7316 0.395383
## PC4:Block 3 0.6386 0.21288 3.1727 0.029658 *
## rich:Block 3 0.0859 0.02865 0.4269 0.734337
## Trt:Block 3 0.4349 0.14498 2.1607 0.100663
## PC4:rich:Trt 1 0.0011 0.00108 0.0160 0.899568
## PC4:rich:Block 3 0.1313 0.04378 0.6525 0.584157
## PC4:Trt:Block 3 0.1802 0.06006 0.8951 0.448329
## rich:Trt:Block 3 0.6664 0.22212 3.3103 0.025136 *
## Residuals 68 4.5627 0.06710
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Significant PC4:Block
# PC4:Block
# Trt:Block
# rich:TRT:Block
# PC4:rich:TRT:Block
# Block
# PC3 and simpson
simPC1<-(lm(RelativeFitness~PC1*sim*TRT*Block-PC1:sim:TRT:Block,RootFitAlpha))
anova(simPC1)## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## PC1 1 0.1572 0.15720 2.6464 0.10841
## sim 1 0.1068 0.10681 1.7981 0.18440
## TRT 1 0.0331 0.03309 0.5571 0.45800
## Block 3 7.9690 2.65634 44.7194 4.455e-16 ***
## PC1:sim 1 0.0568 0.05682 0.9565 0.33154
## PC1:TRT 1 0.0086 0.00855 0.1440 0.70551
## sim:TRT 1 0.0259 0.02592 0.4364 0.51109
## PC1:Block 3 0.6054 0.20180 3.3973 0.02265 *
## sim:Block 3 0.0056 0.00188 0.0317 0.99234
## TRT:Block 3 0.1548 0.05159 0.8686 0.46178
## PC1:sim:TRT 1 0.0233 0.02327 0.3918 0.53344
## PC1:sim:Block 3 0.1336 0.04454 0.7498 0.52623
## PC1:TRT:Block 3 1.4721 0.49069 8.2608 9.202e-05 ***
## sim:TRT:Block 3 0.2723 0.09075 1.5278 0.21518
## Residuals 68 4.0392 0.05940
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# PC1:TRT:Block Significant
# PC1:Block
# Block
# PC2 and simpson
simPC2<-(lm(RelativeFitness~PC2*sim*TRT*Block-PC2:sim:TRT:Block,RootFitAlpha))
anova(simPC2)## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## PC2 1 0.0335 0.03349 0.5049 0.4798031
## sim 1 0.1283 0.12825 1.9333 0.1689337
## TRT 1 0.1738 0.17376 2.6192 0.1102051
## Block 3 7.8984 2.63279 39.6873 6.111e-15 ***
## PC2:sim 1 0.0018 0.00185 0.0279 0.8679312
## PC2:TRT 1 0.0340 0.03399 0.5124 0.4765544
## sim:TRT 1 0.0002 0.00023 0.0035 0.9529224
## PC2:Block 3 0.1113 0.03710 0.5593 0.6437035
## sim:Block 3 0.0173 0.00577 0.0869 0.9669815
## TRT:Block 3 0.2675 0.08918 1.3443 0.2673307
## PC2:sim:TRT 1 0.0002 0.00016 0.0024 0.9609559
## PC2:sim:Block 3 0.3233 0.10775 1.6243 0.1918210
## PC2:TRT:Block 3 1.3067 0.43557 6.5659 0.0005786 ***
## sim:TRT:Block 3 0.2565 0.08549 1.2887 0.2853277
## Residuals 68 4.5110 0.06634
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##
## Call:
## lm(formula = RelativeFitness ~ PC2 * sim * TRT * Block - PC2:sim:TRT:Block,
## data = RootFitAlpha)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.57386 -0.08097 -0.01539 0.07065 0.95971
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.31355 54.25290 0.190 0.84980
## PC2 16.63819 21.60503 0.770 0.44390
## sim -9.90900 55.60967 -0.178 0.85910
## TRTInter -1.46047 55.59757 -0.026 0.97912
## Block2 5.90379 57.53744 0.103 0.91858
## Block3 -42.35539 57.49005 -0.737 0.46381
## Block4 21.37072 54.35342 0.393 0.69542
## PC2:sim -17.00262 22.12012 -0.769 0.44476
## PC2:TRTInter -21.65901 18.94739 -1.143 0.25700
## sim:TRTInter 1.50405 56.99176 0.026 0.97902
## PC2:Block2 10.98674 21.29535 0.516 0.60758
## PC2:Block3 18.73036 20.97436 0.893 0.37500
## PC2:Block4 3.89781 17.58602 0.222 0.82526
## sim:Block2 -5.83751 59.01585 -0.099 0.92150
## sim:Block3 43.88540 58.93391 0.745 0.45905
## sim:Block4 -21.77280 55.71615 -0.391 0.69718
## TRTInter:Block2 -9.57544 59.10553 -0.162 0.87178
## TRTInter:Block3 35.16565 59.38576 0.592 0.55571
## TRTInter:Block4 -35.42532 56.57604 -0.626 0.53331
## PC2:sim:TRTInter 22.11197 19.39931 1.140 0.25835
## PC2:sim:Block2 -11.34609 21.83431 -0.520 0.60500
## PC2:sim:Block3 -19.89275 21.55102 -0.923 0.35924
## PC2:sim:Block4 -4.44916 18.04588 -0.247 0.80600
## PC2:TRTInter:Block2 -0.05497 0.22580 -0.243 0.80837
## PC2:TRTInter:Block3 0.83206 0.29892 2.784 0.00696 **
## PC2:TRTInter:Block4 0.73181 0.29575 2.474 0.01585 *
## sim:TRTInter:Block2 9.72127 60.63200 0.160 0.87309
## sim:TRTInter:Block3 -35.70578 60.87591 -0.587 0.55946
## sim:TRTInter:Block4 36.60244 58.00381 0.631 0.53013
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2576 on 68 degrees of freedom
## Multiple R-squared: 0.7005, Adjusted R-squared: 0.5772
## F-statistic: 5.681 on 28 and 68 DF, p-value: 2.559e-09Model1a<-(lm(RelativeFitness~sim*PC2*Block,RootFitAlpha%>%filter(TRT=="Alone")))
Model1c<-(lm(RelativeFitness~sim*PC2*Block,RootFitAlpha%>%filter(TRT!="Alone")))
summary(Model1a)##
## Call:
## lm(formula = RelativeFitness ~ sim * PC2 * Block, data = RootFitAlpha %>%
## filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.58339 -0.06284 0.00532 0.05732 0.94429
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -102.04 345.26 -0.296 0.775
## sim 105.08 353.39 0.297 0.774
## PC2 -69.47 257.04 -0.270 0.794
## Block2 116.24 348.30 0.334 0.747
## Block3 422.38 399.60 1.057 0.321
## Block4 132.07 346.67 0.381 0.713
## sim:PC2 71.16 263.17 0.270 0.794
## sim:Block2 -118.77 356.52 -0.333 0.748
## sim:Block3 -432.26 409.15 -1.056 0.322
## sim:Block4 -135.03 354.86 -0.381 0.713
## PC2:Block2 93.93 259.54 0.362 0.727
## PC2:Block3 587.87 371.74 1.581 0.152
## PC2:Block4 86.66 259.23 0.334 0.747
## sim:PC2:Block2 -96.25 265.75 -0.362 0.727
## sim:PC2:Block3 -605.03 381.58 -1.586 0.151
## sim:PC2:Block4 -89.14 265.47 -0.336 0.746
##
## Residual standard error: 0.4552 on 8 degrees of freedom
## Multiple R-squared: 0.6971, Adjusted R-squared: 0.1293
## F-statistic: 1.228 on 15 and 8 DF, p-value: 0.3987##
## Call:
## lm(formula = RelativeFitness ~ sim * PC2 * Block, data = RootFitAlpha %>%
## filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.45095 -0.06926 -0.00438 0.06992 0.61829
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.703 5.528 1.574 0.1209
## sim -8.251 5.692 -1.450 0.1526
## PC2 -4.568 7.918 -0.577 0.5663
## Block2 -3.100 9.657 -0.321 0.7494
## Block3 -6.913 8.180 -0.845 0.4016
## Block4 -14.171 7.580 -1.869 0.0667 .
## sim:PC2 4.642 8.163 0.569 0.5718
## sim:Block2 3.298 9.930 0.332 0.7410
## sim:Block3 7.904 8.404 0.941 0.3509
## sim:Block4 14.948 7.814 1.913 0.0608 .
## PC2:Block2 14.494 18.991 0.763 0.4485
## PC2:Block3 12.109 15.918 0.761 0.4500
## PC2:Block4 6.345 14.016 0.453 0.6525
## sim:PC2:Block2 -15.002 19.514 -0.769 0.4452
## sim:PC2:Block3 -12.259 16.323 -0.751 0.4557
## sim:PC2:Block4 -6.217 14.448 -0.430 0.6686
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1939 on 57 degrees of freedom
## Multiple R-squared: 0.7738, Adjusted R-squared: 0.7143
## F-statistic: 13 on 15 and 57 DF, p-value: 2.73e-13# Block sig
# PC2:TRT:Block significant
# PC2:sim:TRT:Block
# Marginal treatment effect
# PC3 and simpson
simPC3<-(lm(RelativeFitness~PC3*sim*TRT*Block-PC3:sim:TRT:Block,RootFitAlpha))
anova(simPC3)# Marginal simpson## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## PC3 1 0.1472 0.14717 2.3049 0.13361
## sim 1 0.1804 0.18043 2.8258 0.09735 .
## TRT 1 0.0262 0.02620 0.4104 0.52393
## Block 3 8.0786 2.69287 42.1739 1.634e-15 ***
## PC3:sim 1 0.0074 0.00740 0.1159 0.73453
## PC3:TRT 1 0.0814 0.08144 1.2755 0.26271
## sim:TRT 1 0.0150 0.01499 0.2348 0.62954
## PC3:Block 3 0.2726 0.09087 1.4231 0.24361
## sim:Block 3 0.0226 0.00754 0.1180 0.94923
## TRT:Block 3 0.6226 0.20754 3.2503 0.02702 *
## PC3:sim:TRT 1 0.2829 0.28292 4.4308 0.03899 *
## PC3:sim:Block 3 0.3339 0.11131 1.7433 0.16639
## PC3:TRT:Block 3 0.6259 0.20862 3.2673 0.02647 *
## sim:TRT:Block 3 0.0250 0.00832 0.1303 0.94174
## Residuals 68 4.3419 0.06385
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# significant Block
# TRT:Block significant
# PC3:sim:TRT significant
# PC3:TRT:Block
summary(simPC3)# Marginal simpson##
## Call:
## lm(formula = RelativeFitness ~ PC3 * sim * TRT * Block - PC3:sim:TRT:Block,
## data = RootFitAlpha)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.66880 -0.08737 -0.00250 0.08177 0.85270
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -14.2234 52.8303 -0.269 0.7886
## PC3 -8.8564 47.7361 -0.186 0.8534
## sim 15.1878 54.1353 0.281 0.7799
## TRTInter 21.2688 54.0330 0.394 0.6951
## Block2 17.5956 49.0732 0.359 0.7210
## Block3 23.2894 56.4491 0.413 0.6812
## Block4 15.3787 55.9463 0.275 0.7842
## PC3:sim 9.1025 48.9063 0.186 0.8529
## PC3:TRTInter 15.4803 44.7080 0.346 0.7302
## sim:TRTInter -21.7279 55.3673 -0.392 0.6960
## PC3:Block2 -8.3836 34.2032 -0.245 0.8071
## PC3:Block3 -40.6811 44.3192 -0.918 0.3619
## PC3:Block4 26.3229 46.1503 0.570 0.5703
## sim:Block2 -17.8500 50.3477 -0.355 0.7240
## sim:Block3 -23.3692 57.8425 -0.404 0.6875
## sim:Block4 -14.4641 57.4803 -0.252 0.8021
## TRTInter:Block2 -21.6630 46.5786 -0.465 0.6434
## TRTInter:Block3 -24.1818 54.0026 -0.448 0.6557
## TRTInter:Block4 -32.6338 51.6022 -0.632 0.5292
## PC3:sim:TRTInter -15.9966 45.8066 -0.349 0.7280
## PC3:sim:Block2 8.5154 35.0660 0.243 0.8089
## PC3:sim:Block3 41.8959 45.3780 0.923 0.3591
## PC3:sim:Block4 -28.1097 47.4568 -0.592 0.5556
## PC3:TRTInter:Block2 0.3701 0.5201 0.711 0.4792
## PC3:TRTInter:Block3 -0.5185 0.5207 -0.996 0.3229
## PC3:TRTInter:Block4 0.9865 0.5572 1.770 0.0811 .
## sim:TRTInter:Block2 22.0978 47.7920 0.462 0.6453
## sim:TRTInter:Block3 25.1259 55.3294 0.454 0.6512
## sim:TRTInter:Block4 32.5984 52.9859 0.615 0.5405
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2527 on 68 degrees of freedom
## Multiple R-squared: 0.7118, Adjusted R-squared: 0.5931
## F-statistic: 5.997 on 28 and 68 DF, p-value: 8.503e-10Model1a<-(lm(RelativeFitness~sim+PC3,RootFitAlpha%>%filter(TRT=="Alone")))
Model1c<-(lm(RelativeFitness~sim+PC3,RootFitAlpha%>%filter(TRT!="Alone")))
summary(Model1a)##
## Call:
## lm(formula = RelativeFitness ~ sim + PC3, data = RootFitAlpha %>%
## filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.4703 -0.3318 -0.2033 0.2180 1.3272
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.8095 18.2024 -0.099 0.922
## sim 2.9122 18.7096 0.156 0.878
## PC3 -0.1684 0.2014 -0.836 0.413
##
## Residual standard error: 0.5018 on 21 degrees of freedom
## Multiple R-squared: 0.03357, Adjusted R-squared: -0.05847
## F-statistic: 0.3648 on 2 and 21 DF, p-value: 0.6987##
## Call:
## lm(formula = RelativeFitness ~ sim + PC3, data = RootFitAlpha %>%
## filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.46081 -0.35329 -0.01783 0.30299 1.15087
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.09479 4.90169 -0.835 0.406
## sim 5.23823 5.04630 1.038 0.303
## PC3 -0.01693 0.11992 -0.141 0.888
##
## Residual standard error: 0.3651 on 70 degrees of freedom
## Multiple R-squared: 0.0152, Adjusted R-squared: -0.01293
## F-statistic: 0.5404 on 2 and 70 DF, p-value: 0.5849##
## Call:
## lm(formula = RelativeFitness ~ PC4 + sim, data = RootFitAlpha %>%
## filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.4724 -0.2934 -0.1654 0.1092 1.2992
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.3237 18.0686 -0.073 0.942
## PC4 0.1564 0.1520 1.029 0.315
## sim 2.3418 18.5736 0.126 0.901
##
## Residual standard error: 0.4977 on 21 degrees of freedom
## Multiple R-squared: 0.04931, Adjusted R-squared: -0.04123
## F-statistic: 0.5447 on 2 and 21 DF, p-value: 0.588##
## Call:
## lm(formula = RelativeFitness ~ PC4 + sim, data = RootFitAlpha %>%
## filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.43274 -0.35392 -0.02619 0.29020 1.18353
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.59706 4.88686 -0.736 0.464
## PC4 0.05027 0.11832 0.425 0.672
## sim 4.73130 5.02536 0.941 0.350
##
## Residual standard error: 0.3647 on 70 degrees of freedom
## Multiple R-squared: 0.01746, Adjusted R-squared: -0.01061
## F-statistic: 0.6219 on 2 and 70 DF, p-value: 0.5399## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## PC4 1 0.3109 0.31087 4.8750 0.0306243 *
## sim 1 0.0917 0.09169 1.4379 0.2346391
## TRT 1 0.0899 0.08986 1.4092 0.2393243
## Block 3 7.7301 2.57670 40.4069 4.15e-15 ***
## PC4:sim 1 0.0331 0.03313 0.5195 0.4735387
## PC4:TRT 1 0.0007 0.00067 0.0105 0.9187124
## sim:TRT 1 0.0000 0.00000 0.0001 0.9933654
## PC4:Block 3 0.6606 0.22020 3.4531 0.0211804 *
## sim:Block 3 0.0705 0.02349 0.3683 0.7760682
## TRT:Block 3 0.2466 0.08220 1.2891 0.2852120
## PC4:sim:TRT 1 0.0119 0.01192 0.1869 0.6669063
## PC4:sim:Block 3 0.0336 0.01119 0.1755 0.9126001
## PC4:TRT:Block 3 0.1467 0.04889 0.7666 0.5166729
## sim:TRT:Block 3 1.3012 0.43374 6.8018 0.0004456 ***
## Residuals 68 4.3363 0.06377
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Significant PC4
# Significant Block
# Significant PC4:Block
# Significant sim:TRT:Block
# Inv Simp and PC1
InsimPC1<-(lm(RelativeFitness~PC1*InvSimp*TRT*Block-PC1:InvSimp:TRT:Block,RootFitAlpha))
anova(InsimPC1)# Significant InvSimp## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## PC1 1 0.1572 0.15720 2.6049 0.11117
## InvSimp 1 0.3077 0.30773 5.0993 0.02715 *
## TRT 1 0.0280 0.02802 0.4643 0.49792
## Block 3 7.7693 2.58976 42.9143 1.114e-15 ***
## PC1:InvSimp 1 0.0200 0.01995 0.3306 0.56720
## PC1:TRT 1 0.0072 0.00720 0.1194 0.73078
## InvSimp:TRT 1 0.0112 0.01125 0.1864 0.66730
## PC1:Block 3 0.6440 0.21467 3.5573 0.01870 *
## InvSimp:Block 3 0.0069 0.00232 0.0384 0.98987
## TRT:Block 3 0.1715 0.05716 0.9472 0.42282
## PC1:InvSimp:TRT 1 0.0105 0.01045 0.1732 0.67860
## PC1:InvSimp:Block 3 0.1621 0.05403 0.8952 0.44823
## PC1:TRT:Block 3 1.5731 0.52437 8.6892 5.861e-05 ***
## InvSimp:TRT:Block 3 0.0913 0.03044 0.5044 0.68051
## Residuals 68 4.1036 0.06035
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Significant Block
# Inv Simp and PC2
InsimPC2<-(lm(RelativeFitness~PC2*InvSimp*TRT*Block-PC2:InvSimp:TRT:Block,RootFitAlpha))
anova(InsimPC2)# Significant InvSimp## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## PC2 1 0.0335 0.03349 0.5031 0.480569
## InvSimp 1 0.3449 0.34489 5.1808 0.025991 *
## TRT 1 0.1493 0.14929 2.2425 0.138889
## Block 3 7.7050 2.56833 38.5804 1.118e-14 ***
## PC2:InvSimp 1 0.0066 0.00664 0.0998 0.753045
## PC2:TRT 1 0.0374 0.03743 0.5622 0.455949
## InvSimp:TRT 1 0.0012 0.00123 0.0184 0.892412
## PC2:Block 3 0.1192 0.03972 0.5966 0.619390
## InvSimp:Block 3 0.0322 0.01072 0.1610 0.922207
## TRT:Block 3 0.2806 0.09352 1.4048 0.248918
## PC2:InvSimp:TRT 1 0.0000 0.00003 0.0004 0.983368
## PC2:InvSimp:Block 3 0.2563 0.08543 1.2833 0.287137
## PC2:TRT:Block 3 1.1819 0.39397 5.9180 0.001196 **
## InvSimp:TRT:Block 3 0.3888 0.12960 1.9467 0.130301
## Residuals 68 4.5268 0.06657
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Significant Block# Significant Inverse simpson
# Significant Block
# Significant PC2:TRT:Block
# Significant PC2:InvSimp:TRT:Block
# Marginal InvSimp:TRT:Block
# PC3 and Inv Simpson
InsimPC3<-(lm(RelativeFitness~PC3*InvSimp*TRT*Block-PC3:InvSimp:TRT:Block,RootFitAlpha))
anova(lm(RelativeFitness~PC3*InvSimp*TRT+Block,RootFitAlpha))## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## PC3 1 0.1472 0.14717 2.0545 0.15539
## InvSimp 1 0.4312 0.43121 6.0196 0.01617 *
## TRT 1 0.0110 0.01102 0.1539 0.69584
## Block 3 7.8431 2.61437 36.4961 2.607e-15 ***
## PC3:InvSimp 1 0.0296 0.02959 0.4131 0.52212
## PC3:TRT 1 0.0810 0.08095 1.1301 0.29073
## InvSimp:TRT 1 0.0118 0.01182 0.1649 0.68565
## PC3:InvSimp:TRT 1 0.3483 0.34828 4.8619 0.03012 *
## Residuals 86 6.1605 0.07163
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## PC3 1 0.1472 0.14717 2.2663 0.13685
## InvSimp 1 0.4312 0.43121 6.6403 0.01214 *
## TRT 1 0.0110 0.01102 0.1697 0.68165
## Block 3 7.8431 2.61437 40.2593 4.491e-15 ***
## PC3:InvSimp 1 0.0296 0.02959 0.4557 0.50194
## PC3:TRT 1 0.0810 0.08095 1.2466 0.26812
## InvSimp:TRT 1 0.0118 0.01182 0.1820 0.67105
## PC3:Block 3 0.2839 0.09463 1.4572 0.23398
## InvSimp:Block 3 0.0250 0.00832 0.1282 0.94307
## TRT:Block 3 0.6251 0.20835 3.2085 0.02841 *
## PC3:InvSimp:TRT 1 0.3230 0.32301 4.9740 0.02903 *
## PC3:InvSimp:Block 3 0.1879 0.06263 0.9645 0.41463
## PC3:TRT:Block 3 0.6276 0.20921 3.2216 0.02796 *
## InvSimp:TRT:Block 3 0.0206 0.00686 0.1056 0.95654
## Residuals 68 4.4158 0.06494
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Plot marginal means
# Within treatment
Model1a<-(lm(RelativeFitness~InvSimp+PC3,RootFitAlpha%>%filter(TRT=="Alone")))
Model1c<-(lm(RelativeFitness~InvSimp+PC3,RootFitAlpha%>%filter(TRT!="Alone")))
summary(Model1a)##
## Call:
## lm(formula = RelativeFitness ~ InvSimp + PC3, data = RootFitAlpha %>%
## filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.4887 -0.3279 -0.2033 0.2446 1.3108
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.807557 0.571110 1.414 0.172
## InvSimp 0.005734 0.014510 0.395 0.697
## PC3 -0.171933 0.200835 -0.856 0.402
##
## Residual standard error: 0.5003 on 21 degrees of freedom
## Multiple R-squared: 0.0396, Adjusted R-squared: -0.05187
## F-statistic: 0.4329 on 2 and 21 DF, p-value: 0.6543##
## Call:
## lm(formula = RelativeFitness ~ InvSimp + PC3, data = RootFitAlpha %>%
## filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.48730 -0.33829 -0.00749 0.23481 1.14643
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.743057 0.164404 4.52 2.46e-05 ***
## InvSimp 0.006644 0.004206 1.58 0.119
## PC3 -0.037131 0.119838 -0.31 0.758
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3615 on 70 degrees of freedom
## Multiple R-squared: 0.03447, Adjusted R-squared: 0.006882
## F-statistic: 1.249 on 2 and 70 DF, p-value: 0.293# Inv simp and PC4
InsimPC4<-(lm(RelativeFitness~PC4*InvSimp*TRT*Block-PC4:InvSimp:TRT:Block,RootFitAlpha))
anova(InsimPC4)# Significant InvSimp## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## PC4 1 0.3109 0.31087 4.6388 0.034805 *
## InvSimp 1 0.2915 0.29149 4.3495 0.040775 *
## TRT 1 0.0768 0.07676 1.1455 0.288284
## Block 3 7.5424 2.51413 37.5154 2.02e-14 ***
## PC4:InvSimp 1 0.0157 0.01565 0.2335 0.630460
## PC4:TRT 1 0.0009 0.00094 0.0140 0.906228
## InvSimp:TRT 1 0.0000 0.00001 0.0001 0.991107
## PC4:Block 3 0.6935 0.23118 3.4496 0.021270 *
## InvSimp:Block 3 0.0722 0.02405 0.3589 0.782836
## TRT:Block 3 0.3240 0.10800 1.6115 0.194776
## PC4:InvSimp:TRT 1 0.0000 0.00004 0.0006 0.980912
## PC4:InvSimp:Block 3 0.0566 0.01886 0.2814 0.838666
## PC4:TRT:Block 3 0.1333 0.04443 0.6630 0.577670
## InvSimp:TRT:Block 3 0.9889 0.32963 4.9187 0.003757 **
## Residuals 68 4.5571 0.06702
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Significant PC4
# Significant InvSimp
# Significant Block
# Significant PC4:Block
# Significant InvSimp:TRT:Block
# Even and PC1
EvenPC1<-(lm(RelativeFitness~PC1*even*TRT*Block-PC1:even:TRT:Block,RootFitAlpha))
anova(EvenPC1)# Marginal PC1:even:Block## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## PC1 1 0.1572 0.15720 2.5901 0.1121697
## even 1 0.9609 0.96094 15.8329 0.0001705 ***
## TRT 1 0.0945 0.09446 1.5564 0.2164694
## Block 3 7.0450 2.34833 38.6921 1.051e-14 ***
## PC1:even 1 0.0110 0.01097 0.1808 0.6720186
## PC1:TRT 1 0.0073 0.00727 0.1197 0.7304251
## even:TRT 1 0.0291 0.02912 0.4799 0.4908485
## PC1:Block 3 0.4770 0.15899 2.6196 0.0577970 .
## even:Block 3 0.2369 0.07898 1.3013 0.2811621
## TRT:Block 3 0.2228 0.07427 1.2237 0.3078255
## PC1:even:TRT 1 0.0503 0.05032 0.8290 0.3657653
## PC1:even:Block 3 0.4498 0.14993 2.4703 0.0692345 .
## PC1:TRT:Block 3 0.9172 0.30572 5.0372 0.0032749 **
## even:TRT:Block 3 0.2776 0.09254 1.5247 0.2159789
## Residuals 68 4.1271 0.06069
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Significant PC1:TRT:Block
# Significant PC1:Block
# Significant even
# Significant Block
# Even and PC2
EvenPC2<-(lm(RelativeFitness~PC2*even*TRT*Block-PC2:even:TRT:Block,RootFitAlpha))
anova(EvenPC2)# Significant even## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## PC2 1 0.0335 0.03349 0.4791 0.4911911
## even 1 0.9467 0.94674 13.5430 0.0004625 ***
## TRT 1 0.2802 0.28024 4.0088 0.0492548 *
## Block 3 6.9740 2.32466 33.2541 2.399e-13 ***
## PC2:even 1 0.0042 0.00419 0.0599 0.8073384
## PC2:TRT 1 0.0392 0.03923 0.5612 0.4563424
## even:TRT 1 0.0224 0.02240 0.3204 0.5732100
## PC2:Block 3 0.0807 0.02688 0.3846 0.7644415
## even:Block 3 0.2732 0.09107 1.3028 0.2806703
## TRT:Block 3 0.3189 0.10629 1.5205 0.2170625
## PC2:even:TRT 1 0.0049 0.00488 0.0698 0.7924102
## PC2:even:Block 3 0.2932 0.09772 1.3979 0.2509731
## PC2:TRT:Block 3 0.9836 0.32787 4.6901 0.0049017 **
## even:TRT:Block 3 0.0554 0.01846 0.2641 0.8510158
## Residuals 68 4.7536 0.06991
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Significant Treatment
# Significant Block
# Significant PC2:TRT:Block
# Significant PC2:even:TRT:Block
# Even and PC3
EvenPC3<-(lm(RelativeFitness~PC3*even*TRT*Block-PC3:even:TRT:Block,RootFitAlpha))
anova(EvenPC3)# Significant even## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## PC3 1 0.1472 0.14717 2.4716 0.1205639
## even 1 1.0146 1.01457 17.0387 0.0001022 ***
## TRT 1 0.0887 0.08870 1.4896 0.2264958
## Block 3 7.1871 2.39570 40.2335 4.554e-15 ***
## PC3:even 1 0.0068 0.00678 0.1139 0.7368152
## PC3:TRT 1 0.0789 0.07894 1.3257 0.2536128
## even:TRT 1 0.0032 0.00319 0.0535 0.8177823
## PC3:Block 3 0.3195 0.10650 1.7885 0.1575917
## even:Block 3 0.3035 0.10115 1.6987 0.1754996
## TRT:Block 3 0.6117 0.20389 3.4241 0.0219302 *
## PC3:even:TRT 1 0.1565 0.15650 2.6283 0.1096001
## PC3:even:Block 3 0.5204 0.17347 2.9133 0.0405360 *
## PC3:TRT:Block 3 0.4101 0.13670 2.2957 0.0855056 .
## even:TRT:Block 3 0.1666 0.05552 0.9324 0.4299097
## Residuals 68 4.0491 0.05954
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Significant Block
# Significant TRT:Block
# Significant PC3:even:Block
# Marginal PC3:TRT:Block
# Within treatment
Model1a<-(lm(RelativeFitness~even+PC3,RootFitAlpha%>%filter(TRT=="Alone")))
Model1c<-(lm(RelativeFitness~even+PC3,RootFitAlpha%>%filter(TRT!="Alone")))
summary(Model1a)##
## Call:
## lm(formula = RelativeFitness ~ even + PC3, data = RootFitAlpha %>%
## filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.4972 -0.3149 -0.1819 0.1996 1.2059
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.7658 2.2808 1.651 0.114
## even -271.0769 224.9026 -1.205 0.241
## PC3 -0.1177 0.1994 -0.590 0.562
##
## Residual standard error: 0.4856 on 21 degrees of freedom
## Multiple R-squared: 0.09506, Adjusted R-squared: 0.008876
## F-statistic: 1.103 on 2 and 21 DF, p-value: 0.3504##
## Call:
## lm(formula = RelativeFitness ~ even + PC3, data = RootFitAlpha %>%
## filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.57479 -0.27236 -0.02728 0.22361 1.11679
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.18830 0.95158 3.351 0.0013 **
## even -211.15458 91.43659 -2.309 0.0239 *
## PC3 -0.01613 0.11479 -0.140 0.8887
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3547 on 70 degrees of freedom
## Multiple R-squared: 0.07083, Adjusted R-squared: 0.04429
## F-statistic: 2.668 on 2 and 70 DF, p-value: 0.07643# Even and PC4
EvenPC4<-(lm(RelativeFitness~PC4*even*TRT*Block-PC4:even:TRT:Block,RootFitAlpha))
anova(EvenPC4)# Significant even## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## PC4 1 0.3109 0.31087 4.2821 0.042319 *
## even 1 0.8223 0.82234 11.3272 0.001259 **
## TRT 1 0.1823 0.18226 2.5105 0.117730
## Block 3 6.9100 2.30333 31.7271 6.092e-13 ***
## PC4:even 1 0.0743 0.07430 1.0235 0.315286
## PC4:TRT 1 0.0021 0.00208 0.0287 0.865948
## even:TRT 1 0.0513 0.05127 0.7063 0.403628
## PC4:Block 3 0.6478 0.21594 2.9745 0.037651 *
## even:Block 3 0.1242 0.04140 0.5703 0.636507
## TRT:Block 3 0.4215 0.14049 1.9352 0.132121
## PC4:even:TRT 1 0.0004 0.00036 0.0049 0.944195
## PC4:even:Block 3 0.1952 0.06506 0.8962 0.447761
## PC4:TRT:Block 3 0.0771 0.02570 0.3539 0.786425
## even:TRT:Block 3 0.3077 0.10258 1.4130 0.246537
## Residuals 68 4.9367 0.07260
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Significant PC4
# Marginal TRT
# Significant Block
# PC4:Block
# Marginal Block:TRT
# Significant PC4:even:TRT:Block
# Within treatment
Model1a<-(lm(RelativeFitness~even*PC4,RootFitAlpha%>%filter(TRT=="Alone")))
Model1c<-(lm(RelativeFitness~even*PC4,RootFitAlpha%>%filter(TRT!="Alone")))
summary(Model1a)##
## Call:
## lm(formula = RelativeFitness ~ even * PC4, data = RootFitAlpha %>%
## filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.5169 -0.2779 -0.1566 0.1333 1.2017
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.6016 2.4358 1.479 0.155
## even -259.5063 237.7250 -1.092 0.288
## PC4 0.5432 3.7641 0.144 0.887
## even:PC4 -40.6631 367.1100 -0.111 0.913
##
## Residual standard error: 0.4931 on 20 degrees of freedom
## Multiple R-squared: 0.1112, Adjusted R-squared: -0.02212
## F-statistic: 0.8341 on 3 and 20 DF, p-value: 0.4909##
## Call:
## lm(formula = RelativeFitness ~ even * PC4, data = RootFitAlpha %>%
## filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.53841 -0.26938 -0.02512 0.22753 1.14471
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.2467 1.1027 2.944 0.00441 **
## even -216.7975 106.6981 -2.032 0.04602 *
## PC4 0.5779 2.8706 0.201 0.84105
## even:PC4 -53.3633 275.2950 -0.194 0.84687
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3571 on 69 degrees of freedom
## Multiple R-squared: 0.07156, Adjusted R-squared: 0.03119
## F-statistic: 1.773 on 3 and 69 DF, p-value: 0.1605##
## Attaching package: 'jtools'## The following object is masked from 'package:Hmisc':
##
## %nin%# Scale the microbial variables
RootFitAlpha$richScaled<-scale(RootFitAlpha$rich)
RootFitAlpha$SimScaled<-scale(RootFitAlpha$sim)
RootFitAlpha$InvSimScaled<-scale(RootFitAlpha$InvSimp)
RootFitAlpha$EvenScaled<-scale(RootFitAlpha$even)
# Phenotypic selection UNIVARIATE
summary(lm(RelativeFitness~PC1,RootFitAlpha%>%filter(TRT=="Alone"))) ##
## Call:
## lm(formula = RelativeFitness ~ PC1, data = RootFitAlpha %>% filter(TRT ==
## "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.65460 -0.26942 -0.09513 0.25049 1.09128
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.04144 0.14836 7.020 4.81e-07 ***
## PC1 0.09390 0.08143 1.153 0.261
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4843 on 22 degrees of freedom
## Multiple R-squared: 0.057, Adjusted R-squared: 0.01413
## F-statistic: 1.33 on 1 and 22 DF, p-value: 0.2612##
## Call:
## lm(formula = RelativeFitness ~ PC1, data = RootFitAlpha %>% filter(TRT !=
## "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.42418 -0.34678 -0.01929 0.32625 1.17732
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.99647 0.04299 23.177 <2e-16 ***
## PC1 -0.02824 0.05666 -0.498 0.62
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3647 on 71 degrees of freedom
## Multiple R-squared: 0.003485, Adjusted R-squared: -0.01055
## F-statistic: 0.2483 on 1 and 71 DF, p-value: 0.6198##
## Call:
## lm(formula = RelativeFitness ~ PC1, data = RootFitAlpha)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.55731 -0.34752 -0.07482 0.25951 1.18858
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.98401 0.04142 23.757 <2e-16 ***
## PC1 0.03701 0.03698 1.001 0.319
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3961 on 95 degrees of freedom
## Multiple R-squared: 0.01044, Adjusted R-squared: 1.908e-05
## F-statistic: 1.002 on 1 and 95 DF, p-value: 0.3194##
## Call:
## lm(formula = RelativeFitness ~ PC2, data = RootFitAlpha %>% filter(TRT ==
## "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.48811 -0.35822 -0.09721 0.15910 1.28637
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.90207 0.10971 8.222 3.74e-08 ***
## PC2 -0.02241 0.07852 -0.285 0.778
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4978 on 22 degrees of freedom
## Multiple R-squared: 0.00369, Adjusted R-squared: -0.0416
## F-statistic: 0.08148 on 1 and 22 DF, p-value: 0.778##
## Call:
## lm(formula = RelativeFitness ~ PC2, data = RootFitAlpha %>% filter(TRT !=
## "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.44699 -0.34284 -0.07087 0.31496 1.21855
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.99395 0.04258 23.344 <2e-16 ***
## PC2 -0.05703 0.07374 -0.773 0.442
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3638 on 71 degrees of freedom
## Multiple R-squared: 0.008356, Adjusted R-squared: -0.005611
## F-statistic: 0.5983 on 1 and 71 DF, p-value: 0.4418##
## Call:
## lm(formula = RelativeFitness ~ PC2, data = RootFitAlpha)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.5567 -0.3417 -0.0957 0.3036 1.2174
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.97126 0.04086 23.77 <2e-16 ***
## PC2 -0.02194 0.04769 -0.46 0.647
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3978 on 95 degrees of freedom
## Multiple R-squared: 0.002223, Adjusted R-squared: -0.00828
## F-statistic: 0.2117 on 1 and 95 DF, p-value: 0.6465##
## Call:
## lm(formula = RelativeFitness ~ PC4, data = RootFitAlpha %>% filter(TRT ==
## "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.47062 -0.29680 -0.16660 0.09031 1.30907
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.9543 0.1064 8.971 8.37e-09 ***
## PC4 0.1573 0.1484 1.060 0.301
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4865 on 22 degrees of freedom
## Multiple R-squared: 0.04859, Adjusted R-squared: 0.005349
## F-statistic: 1.124 on 1 and 22 DF, p-value: 0.3006##
## Call:
## lm(formula = RelativeFitness ~ PC4, data = RootFitAlpha %>% filter(TRT !=
## "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.41271 -0.35334 -0.02464 0.28524 1.19788
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.00364 0.04565 21.985 <2e-16 ***
## PC4 0.06965 0.11642 0.598 0.552
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3644 on 71 degrees of freedom
## Multiple R-squared: 0.005016, Adjusted R-squared: -0.008998
## F-statistic: 0.358 on 1 and 71 DF, p-value: 0.5515##
## Call:
## lm(formula = RelativeFitness ~ PC4, data = RootFitAlpha)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.49562 -0.32506 -0.09444 0.27099 1.25420
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.99474 0.04259 23.357 <2e-16 ***
## PC4 0.12228 0.08642 1.415 0.16
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3941 on 95 degrees of freedom
## Multiple R-squared: 0.02064, Adjusted R-squared: 0.01033
## F-statistic: 2.002 on 1 and 95 DF, p-value: 0.1604##
## Call:
## lm(formula = RelativeFitness ~ PC3, data = RootFitAlpha %>% filter(TRT ==
## "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.4600 -0.3594 -0.2105 0.1988 1.3395
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.0236 0.1623 6.308 2.39e-06 ***
## PC3 -0.1691 0.1968 -0.859 0.4
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4906 on 22 degrees of freedom
## Multiple R-squared: 0.03246, Adjusted R-squared: -0.01152
## F-statistic: 0.738 on 1 and 22 DF, p-value: 0.3996##
## Call:
## lm(formula = RelativeFitness ~ PC3, data = RootFitAlpha %>% filter(TRT !=
## "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.42122 -0.35018 -0.02809 0.32572 1.18028
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.993125 0.044859 22.139 <2e-16 ***
## PC3 0.006728 0.117799 0.057 0.955
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3653 on 71 degrees of freedom
## Multiple R-squared: 4.594e-05, Adjusted R-squared: -0.01404
## F-statistic: 0.003262 on 1 and 71 DF, p-value: 0.9546##
## Call:
## lm(formula = RelativeFitness ~ PC3, data = RootFitAlpha)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.49194 -0.35042 -0.07094 0.24924 1.28521
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.99481 0.04557 21.832 <2e-16 ***
## PC3 -0.08377 0.08653 -0.968 0.335
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3963 on 95 degrees of freedom
## Multiple R-squared: 0.00977, Adjusted R-squared: -0.0006537
## F-statistic: 0.9373 on 1 and 95 DF, p-value: 0.3354##
## Call:
## lm(formula = RelativeFitness ~ EvenScaled, data = RootFitAlpha %>%
## filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.5431 -0.3424 -0.1684 0.2188 1.1555
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.88137 0.10043 8.776 1.23e-08 ***
## EvenScaled -0.13811 0.09981 -1.384 0.18
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4784 on 22 degrees of freedom
## Multiple R-squared: 0.08006, Adjusted R-squared: 0.03825
## F-statistic: 1.915 on 1 and 22 DF, p-value: 0.1803##
## Call:
## lm(formula = RelativeFitness ~ EvenScaled, data = RootFitAlpha %>%
## filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.55993 -0.26890 -0.02759 0.21735 1.13118
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.00140 0.04135 24.219 <2e-16 ***
## EvenScaled -0.09687 0.04172 -2.322 0.0231 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3522 on 71 degrees of freedom
## Multiple R-squared: 0.07057, Adjusted R-squared: 0.05748
## F-statistic: 5.391 on 1 and 71 DF, p-value: 0.02311## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## EvenScaled 1 0.9647 0.96469 6.4818 0.01254 *
## TRT 1 0.2283 0.22826 1.5337 0.21868
## EvenScaled:TRT 1 0.0295 0.02954 0.1985 0.65700
## Residuals 93 13.8412 0.14883
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##
## Call:
## lm(formula = RelativeFitness ~ SimScaled, data = RootFitAlpha %>%
## filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.4787 -0.3672 -0.1385 0.1897 1.2711
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.91175 0.10245 8.899 9.64e-09 ***
## SimScaled 0.02616 0.14886 0.176 0.862
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4984 on 22 degrees of freedom
## Multiple R-squared: 0.001402, Adjusted R-squared: -0.04399
## F-statistic: 0.03089 on 1 and 22 DF, p-value: 0.8621##
## Call:
## lm(formula = RelativeFitness ~ SimScaled, data = RootFitAlpha %>%
## filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.44546 -0.35291 -0.02388 0.30147 1.16595
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.99500 0.04245 23.439 <2e-16 ***
## SimScaled 0.04089 0.03943 1.037 0.303
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3626 on 71 degrees of freedom
## Multiple R-squared: 0.01492, Adjusted R-squared: 0.00105
## F-statistic: 1.076 on 1 and 71 DF, p-value: 0.3032## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## SimScaled 1 0.1346 0.134644 0.8461 0.3600
## TRT 1 0.1280 0.127955 0.8041 0.3722
## SimScaled:TRT 1 0.0021 0.002147 0.0135 0.9078
## Residuals 93 14.7989 0.159128##
## Call:
## lm(formula = RelativeFitness ~ InvSimScaled, data = RootFitAlpha %>%
## filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.4985 -0.3568 -0.1458 0.2132 1.2573
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.9155 0.1016 9.012 7.74e-09 ***
## InvSimScaled 0.0512 0.1396 0.367 0.717
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4972 on 22 degrees of freedom
## Multiple R-squared: 0.006081, Adjusted R-squared: -0.0391
## F-statistic: 0.1346 on 1 and 22 DF, p-value: 0.7172##
## Call:
## lm(formula = RelativeFitness ~ InvSimScaled, data = RootFitAlpha %>%
## filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.48452 -0.34071 -0.03188 0.25939 1.17882
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.99326 0.04205 23.62 <2e-16 ***
## InvSimScaled 0.06141 0.03936 1.56 0.123
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3592 on 71 degrees of freedom
## Multiple R-squared: 0.03314, Adjusted R-squared: 0.01953
## F-statistic: 2.434 on 1 and 71 DF, p-value: 0.1232## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## InvSimScaled 1 0.3534 0.35338 2.2509 0.1369
## TRT 1 0.1085 0.10847 0.6909 0.4080
## InvSimScaled:TRT 1 0.0011 0.00115 0.0073 0.9320
## Residuals 93 14.6007 0.15700##
## Call:
## lm(formula = RelativeFitness ~ rich, data = RootFitAlpha %>%
## filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.5235 -0.3408 -0.1732 0.2074 1.1566
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.784092 1.427398 -0.549 0.588
## rich 0.003734 0.003132 1.192 0.246
##
## Residual standard error: 0.4834 on 22 degrees of freedom
## Multiple R-squared: 0.06071, Adjusted R-squared: 0.01801
## F-statistic: 1.422 on 1 and 22 DF, p-value: 0.2458##
## Call:
## lm(formula = RelativeFitness ~ rich, data = RootFitAlpha %>%
## filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.53579 -0.29469 -0.01234 0.22797 1.13305
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.255525 0.572115 -0.447 0.6565
## rich 0.002806 0.001281 2.190 0.0318 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3536 on 71 degrees of freedom
## Multiple R-squared: 0.06326, Adjusted R-squared: 0.05006
## F-statistic: 4.794 on 1 and 71 DF, p-value: 0.03184##
## Call:
## lm(formula = RelativeFitness ~ rich, data = RootFitAlpha)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.59124 -0.31236 -0.00207 0.23594 1.15892
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.299358 0.545241 -0.549 0.5843
## rich 0.002845 0.001215 2.342 0.0213 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3872 on 95 degrees of freedom
## Multiple R-squared: 0.05457, Adjusted R-squared: 0.04462
## F-statistic: 5.483 on 1 and 95 DF, p-value: 0.02129## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## rich 1 0.8220 0.82204 5.4543 0.02167 *
## TRT 1 0.2096 0.20957 1.3905 0.24133
## rich:TRT 1 0.0156 0.01563 0.1037 0.74812
## Residuals 93 14.0164 0.15071
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# ANCOVA MUltivariate Selection
# ANCOVA<-(lm(RelativeFitness~TRT+Block+TRT:Block+PC1*Block+PC2*Block+PC3*Block+PC4*Block+richScaled*Block+InvSimScaled*Block+EvenScaled*Block+PC1*TRT*Block+PC2*TRT*Block+PC3*TRT*Block+PC4*TRT*Block+richScaled*TRT*Block+InvSimScaled*TRT*Block+EvenScaled*TRT*Block,RootFitAlpha)) # Full model w Trt by Block interactions per vars
ANCOVA<-(lm(RelativeFitness~TRT+Block+TRT:Block+PC1*TRT+PC2*TRT+PC3*TRT+PC4*TRT+richScaled*TRT+InvSimScaled*TRT+EvenScaled*TRT+PC1*Block+PC2*Block+PC3*Block+PC4*Block+richScaled*Block+InvSimScaled*Block+EvenScaled*Block,RootFitAlpha)) # Full model reported
# Step wise backward regression
library(MASS)
step<-stepAIC(ANCOVA,direction = "backward",trace=FALSE)
step$anova## Stepwise Model Path
## Analysis of Deviance Table
##
## Initial Model:
## RelativeFitness ~ TRT + Block + TRT:Block + PC1 * TRT + PC2 *
## TRT + PC3 * TRT + PC4 * TRT + richScaled * TRT + InvSimScaled *
## TRT + EvenScaled * TRT + PC1 * Block + PC2 * Block + PC3 *
## Block + PC4 * Block + richScaled * Block + InvSimScaled *
## Block + EvenScaled * Block
##
## Final Model:
## RelativeFitness ~ TRT + Block + PC1 + PC2 + PC3 + PC4 + richScaled +
## InvSimScaled + EvenScaled + TRT:Block + TRT:PC1 + TRT:PC3 +
## TRT:richScaled + TRT:EvenScaled + Block:PC1 + Block:PC2 +
## Block:PC3 + Block:PC4 + Block:richScaled + Block:InvSimScaled +
## Block:EvenScaled
##
##
## Step Df Deviance Resid. Df Resid. Dev AIC
## 1 54 3.404728 -238.9059
## 2 - TRT:PC4 1 0.004318070 55 3.409046 -240.7830
## 3 - TRT:InvSimScaled 1 0.004653243 56 3.413700 -242.6507
## 4 - TRT:PC2 1 0.020806204 57 3.434506 -244.0613model<-lm(RelativeFitness ~ TRT + Block + PC1 + PC2 + PC3 + PC4 + richScaled +
InvSimScaled + EvenScaled + TRT:Block + TRT:PC1 + TRT:PC3 +
TRT:richScaled + TRT:EvenScaled + Block:PC1 + Block:PC2 +
Block:PC3 + Block:PC4 + Block:richScaled + Block:InvSimScaled +
Block:EvenScaled,RootFitAlpha
)
# anova(model) # Type I sum of squres--sequence order matters, interactions not accounted
car::Anova(model,type="III") # Report the type three sums of squares~## Anova Table (Type III tests)
##
## Response: RelativeFitness
## Sum Sq Df F value Pr(>F)
## (Intercept) 0.2225 1 3.6920 0.059678 .
## TRT 0.0063 1 0.1040 0.748271
## Block 0.8159 3 4.5139 0.006563 **
## PC1 0.0193 1 0.3197 0.574012
## PC2 0.0051 1 0.0849 0.771792
## PC3 0.0000 1 0.0005 0.982541
## PC4 0.0883 1 1.4647 0.231172
## richScaled 0.0449 1 0.7456 0.391506
## InvSimScaled 0.0000 1 0.0000 0.998091
## EvenScaled 0.0057 1 0.0945 0.759674
## TRT:Block 0.2663 3 1.4733 0.231453
## TRT:PC1 0.1905 1 3.1620 0.080705 .
## TRT:PC3 0.1328 1 2.2043 0.143134
## TRT:richScaled 0.4641 1 7.7023 0.007446 **
## TRT:EvenScaled 0.1964 1 3.2599 0.076274 .
## Block:PC1 0.9067 3 5.0159 0.003727 **
## Block:PC2 0.2339 3 1.2942 0.285204
## Block:PC3 0.2449 3 1.3546 0.265867
## Block:PC4 1.1098 3 6.1395 0.001084 **
## Block:richScaled 0.4936 3 2.7309 0.052151 .
## Block:InvSimScaled 0.4500 3 2.4892 0.069456 .
## Block:EvenScaled 0.4861 3 2.6889 0.054807 .
## Residuals 3.4345 57
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##
## Call:
## lm(formula = RelativeFitness ~ TRT + Block + PC1 + PC2 + PC3 +
## PC4 + richScaled + InvSimScaled + EvenScaled + TRT:Block +
## TRT:PC1 + TRT:PC3 + TRT:richScaled + TRT:EvenScaled + Block:PC1 +
## Block:PC2 + Block:PC3 + Block:PC4 + Block:richScaled + Block:InvSimScaled +
## Block:EvenScaled, data = RootFitAlpha)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.45989 -0.10122 0.01903 0.08367 0.54005
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.5644084 0.2937384 1.921 0.05968 .
## TRTInter 0.0976872 0.3029271 0.322 0.74827
## Block2 -0.0333271 0.3315102 -0.101 0.92028
## Block3 0.9303123 0.3620020 2.570 0.01281 *
## Block4 0.6503006 0.3187389 2.040 0.04597 *
## PC1 -0.0589637 0.1042843 -0.565 0.57401
## PC2 0.0251966 0.0864631 0.291 0.77179
## PC3 -0.0048579 0.2210150 -0.022 0.98254
## PC4 0.2866935 0.2368849 1.210 0.23117
## richScaled 0.3804680 0.4406342 0.863 0.39151
## InvSimScaled -0.0005248 0.2183718 -0.002 0.99809
## EvenScaled 0.1056800 0.3438079 0.307 0.75967
## TRTInter:Block2 0.2105048 0.3554575 0.592 0.55605
## TRTInter:Block3 -0.1818244 0.3737280 -0.487 0.62847
## TRTInter:Block4 -0.3291469 0.3338717 -0.986 0.32837
## TRTInter:PC1 0.1766822 0.0993601 1.778 0.08070 .
## TRTInter:PC3 0.2379503 0.1602688 1.485 0.14313
## TRTInter:richScaled -0.7041574 0.2537230 -2.775 0.00745 **
## TRTInter:EvenScaled -0.4258074 0.2358355 -1.806 0.07627 .
## Block2:PC1 -0.1922776 0.1475096 -1.303 0.19765
## Block3:PC1 0.1606998 0.1310276 1.226 0.22507
## Block4:PC1 -0.2092075 0.1357794 -1.541 0.12890
## Block2:PC2 -0.1881294 0.1208516 -1.557 0.12508
## Block3:PC2 0.0233480 0.1409315 0.166 0.86900
## Block4:PC2 -0.1370329 0.1153875 -1.188 0.23992
## Block2:PC3 -0.2827958 0.2791032 -1.013 0.31523
## Block3:PC3 -0.3696423 0.2752071 -1.343 0.18455
## Block4:PC3 -0.4885016 0.2479188 -1.970 0.05366 .
## Block2:PC4 -0.0781221 0.2666283 -0.293 0.77059
## Block3:PC4 -0.8631692 0.2843812 -3.035 0.00362 **
## Block4:PC4 -0.4061012 0.2680725 -1.515 0.13533
## Block2:richScaled 0.1019838 0.5995899 0.170 0.86554
## Block3:richScaled -0.3168643 0.5909213 -0.536 0.59389
## Block4:richScaled 1.1663541 0.4998220 2.334 0.02317 *
## Block2:InvSimScaled 0.0560490 0.3074563 0.182 0.85599
## Block3:InvSimScaled 0.2484597 0.3004664 0.827 0.41173
## Block4:InvSimScaled -0.5537672 0.2996460 -1.848 0.06978 .
## Block2:EvenScaled 0.1496708 0.4204558 0.356 0.72318
## Block3:EvenScaled -0.1359585 0.4642850 -0.293 0.77071
## Block4:EvenScaled 0.9890849 0.3924176 2.520 0.01454 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2455 on 57 degrees of freedom
## Multiple R-squared: 0.772, Adjusted R-squared: 0.616
## F-statistic: 4.949 on 39 and 57 DF, p-value: 2.921e-08# summary(ANCOVA)
#model2<-lm(RelativeFitness ~ TRT + Block + PC1 + PC2 + PC3 + PC4 + richScaled + InvSimScaled + EvenScaled + TRT:Block + Block:PC1 + Block:PC2 + Block:PC3 + Block:PC4 + Block:richScaled + Block:InvSimScaled + Block:EvenScaled + TRT:PC1 + TRT:PC2 + TRT:PC3 + TRT:PC4 + TRT:Block:PC1 + TRT:Block:PC2 + TRT:Block:PC3 + TRT:Block:PC4,RootFitAlpha)
#interact_plot(ANCOVA,pred=PC1,modx=TRT,partial.residuals=TRUE)
# Multivariate phenotypic selection
# Within treatment
summary(lm(RelativeFitness~PC1+PC2+PC3+PC4+richScaled+InvSimScaled+EvenScaled,RootFitAlpha%>%filter(TRT=="Alone"))) # Alone##
## Call:
## lm(formula = RelativeFitness ~ PC1 + PC2 + PC3 + PC4 + richScaled +
## InvSimScaled + EvenScaled, data = RootFitAlpha %>% filter(TRT ==
## "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.64910 -0.35948 0.00188 0.10703 1.07359
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.17635 0.26534 4.433 0.000417 ***
## PC1 0.11957 0.10004 1.195 0.249447
## PC2 -0.06590 0.10047 -0.656 0.521187
## PC3 -0.09312 0.24367 -0.382 0.707371
## PC4 0.28170 0.19059 1.478 0.158807
## richScaled -0.48344 1.00200 -0.482 0.636005
## InvSimScaled 0.21564 0.51604 0.418 0.681594
## EvenScaled -0.46886 0.74682 -0.628 0.538991
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5084 on 16 degrees of freedom
## Multiple R-squared: 0.2441, Adjusted R-squared: -0.08658
## F-statistic: 0.7382 on 7 and 16 DF, p-value: 0.6438summary(lm(RelativeFitness~PC1+PC2+PC3+PC4+richScaled+InvSimScaled+EvenScaled,RootFitAlpha%>%filter(TRT!="Alone"))) # Competition##
## Call:
## lm(formula = RelativeFitness ~ PC1 + PC2 + PC3 + PC4 + richScaled +
## InvSimScaled + EvenScaled, data = RootFitAlpha %>% filter(TRT !=
## "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.55765 -0.25407 -0.00441 0.20807 1.15789
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.03219 0.05063 20.386 <2e-16 ***
## PC1 -0.08358 0.07419 -1.127 0.264
## PC2 -0.07021 0.10556 -0.665 0.508
## PC3 -0.14197 0.15178 -0.935 0.353
## PC4 0.09987 0.14862 0.672 0.504
## richScaled -0.27359 0.22559 -1.213 0.230
## InvSimScaled 0.18017 0.11452 1.573 0.121
## EvenScaled -0.28159 0.16822 -1.674 0.099 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3542 on 65 degrees of freedom
## Multiple R-squared: 0.1396, Adjusted R-squared: 0.04692
## F-statistic: 1.506 on 7 and 65 DF, p-value: 0.1808##
## Call:
## lm(formula = RelativeFitness ~ rich, data = RootFitAlpha %>%
## filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.5235 -0.3408 -0.1732 0.2074 1.1566
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.784092 1.427398 -0.549 0.588
## rich 0.003734 0.003132 1.192 0.246
##
## Residual standard error: 0.4834 on 22 degrees of freedom
## Multiple R-squared: 0.06071, Adjusted R-squared: 0.01801
## F-statistic: 1.422 on 1 and 22 DF, p-value: 0.2458##
## Call:
## lm(formula = RelativeFitness ~ rich, data = RootFitAlpha %>%
## filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.53579 -0.29469 -0.01234 0.22797 1.13305
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.255525 0.572115 -0.447 0.6565
## rich 0.002806 0.001281 2.190 0.0318 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3536 on 71 degrees of freedom
## Multiple R-squared: 0.06326, Adjusted R-squared: 0.05006
## F-statistic: 4.794 on 1 and 71 DF, p-value: 0.03184# plot
ggplot(data=RootFitAlpha,aes(rich,RelativeFitness,color=TRT))+
geom_point(alpha=0.5,size=3) +
geom_smooth(method=lm, se=FALSE, fullrange=TRUE,size=2)+
theme_classic()+
xlab("Richness")+
Tx+
theme(axis.text.x = element_text(angle=0,hjust = 0.5),axis.text=element_text(color="black",size=15))+
scale_color_manual(values = c("#d8b365","#5ab4ac"),"Treatment", labels = c("Alone", "Competition"))+
theme(legend.position = c(0.2, 0.9))## `geom_smooth()` using formula 'y ~ x'
# Plot
EvenPlot1<-ggplot()+
geom_point(data=RootFitAlpha%>%filter(TRT=="Alone"),aes(EvenScaled,RelativeFitness),size=3,alpha=0.5)+
# geom_smooth(data=RootFitAlpha%>%filter(TRT=="Alone"),aes(even,RelativeFitness),method="lm",fullrange=TRUE,se=FALSE)+
geom_abline(slope=-0.47,intercept = 1.18,color="blue",size=2)+
theme_classic()+
xlab("Evenness")+
Tx+
theme(axis.text.x = element_text(angle=45),axis.text=element_text(color="black",size=15,vjust = 0.5,hjust=1))+
scale_x_continuous(breaks = scales::pretty_breaks(n = 5))
EvenPlot2<-ggplot()+
geom_point(data=RootFitAlpha%>%filter(TRT=="Inter"),aes(EvenScaled,RelativeFitness),size=3,alpha=0.5)+
# geom_smooth(data=RootFitAlpha%>%filter(TRT=="Inter"),aes(EvenScaled,RelativeFitness),method="lm",fullrange=TRUE,se=FALSE)+
geom_abline(slope=-0.28,intercept = 1.03,color="blue",size=2)+
theme_classic()+
xlab("Evenness")+
Tx+
theme(axis.text.x = element_text(angle=45),axis.text=element_text(color="black",size=15,vjust = 0.5,hjust=1))+
scale_x_continuous(breaks = scales::pretty_breaks(n = 5))
ggplot()+
geom_point(data=RootFitAlpha,aes(EvenScaled,RelativeFitness,color=TRT),size=3,alpha=0.5)+
# geom_smooth(data=RootFitAlpha%>%filter(TRT=="Inter"),aes(EvenScaled,RelativeFitness),method="lm",fullrange=TRUE,se=FALSE)+
geom_abline(slope=-0.47,intercept = 1.18,color="red",size=2,linetype="dashed")+
geom_abline(slope=-0.28,intercept = 1.03,color="black",size=2)+
theme_classic()+
xlab("Evenness")+
Tx2+
theme(axis.text.x = element_text(angle=45),axis.text=element_text(color="black",size=15,vjust = 0.5,hjust=1))+
scale_x_continuous(breaks = scales::pretty_breaks(n = 5)) + scale_color_manual(values = c("red","black"),"Treatment", labels = c("Alone", "Competition"))
#ggarrange(P2.rich,P2.even,P4.Sim,P4.simIn,nrow=2,ncol=2)
cowplot::plot_grid(EvenPlot1,EvenPlot2,align = "hv", ncol = 2,labels =c("A","B"), label_size =22 ,hjust=-9,vjust=2,label_x = -0.16)
Block1<-ggplot()+
geom_point(data=RootFitAlpha%>%filter(Block=="1"),aes(even,RelativeFitness),size=3,alpha=0.5)+
geom_smooth(data=RootFitAlpha%>%filter(Block=="1"),aes(even,RelativeFitness),se=FALSE,method="lm",fullrange=TRUE)+
theme_classic()+
xlab("Eveness")+
Tx+
theme(axis.text.x = element_text(angle=45),axis.text=element_text(color="black",size=15,vjust = 0.5,hjust=1))
Block2<-ggplot()+
geom_point(data=RootFitAlpha%>%filter(Block=="2"),aes(even,RelativeFitness),size=3,alpha=0.5)+
geom_smooth(data=RootFitAlpha%>%filter(Block=="2"),aes(even,RelativeFitness),se=FALSE,method="lm",fullrange=TRUE)+
theme_classic()+
xlab("Eveness")+
Tx+
theme(axis.text.x = element_text(angle=45),axis.text=element_text(color="black",size=15,vjust = 0.5,hjust=1))
Block3<-ggplot()+
geom_point(data=RootFitAlpha%>%filter(Block=="3"),aes(even,RelativeFitness),size=3,alpha=0.5)+
geom_smooth(data=RootFitAlpha%>%filter(Block=="3"),aes(even,RelativeFitness),se=FALSE,method="lm",fullrange=TRUE)+
theme_classic()+
xlab("Eveness")+
Tx+
theme(axis.text.x = element_text(angle=45),axis.text=element_text(color="black",size=15,vjust = 0.5,hjust=1))
Block4<-ggplot()+
geom_point(data=RootFitAlpha%>%filter(Block=="4"),aes(even,RelativeFitness),size=3,alpha=0.5)+
geom_smooth(data=RootFitAlpha%>%filter(Block=="4"),aes(even,RelativeFitness),method="lm",fullrange=TRUE)+
theme_classic()+
xlab("Eveness")+
Tx+
theme(axis.text.x = element_text(angle=45),axis.text=element_text(color="black",size=15,vjust = 0.5,hjust=1))
# Modeling each diversity metric alone w ea root trait
summary(lm(RelativeFitness~PC1+PC2+PC3+PC4+sim,RootFitAlpha%>%filter(TRT=="Alone")))##
## Call:
## lm(formula = RelativeFitness ~ PC1 + PC2 + PC3 + PC4 + sim, data = RootFitAlpha %>%
## filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.64505 -0.33239 -0.03507 0.16828 1.10462
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.65354 19.49486 -0.136 0.893
## PC1 0.11786 0.09723 1.212 0.241
## PC2 -0.06646 0.09724 -0.683 0.503
## PC3 -0.09046 0.21132 -0.428 0.674
## PC4 0.28639 0.17811 1.608 0.125
## sim 3.93219 20.00809 0.197 0.846
##
## Residual standard error: 0.4962 on 18 degrees of freedom
## Multiple R-squared: 0.19, Adjusted R-squared: -0.03499
## F-statistic: 0.8445 on 5 and 18 DF, p-value: 0.5359##
## Call:
## lm(formula = RelativeFitness ~ PC1 + PC2 + PC3 + PC4 + sim, data = RootFitAlpha %>%
## filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.43898 -0.30872 -0.03749 0.25095 1.17923
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.54213 5.05606 -0.898 0.372
## PC1 -0.10647 0.07433 -1.432 0.157
## PC2 -0.10829 0.10740 -1.008 0.317
## PC3 -0.13152 0.15697 -0.838 0.405
## PC4 0.10315 0.15161 0.680 0.499
## sim 5.73704 5.20506 1.102 0.274
##
## Residual standard error: 0.3661 on 67 degrees of freedom
## Multiple R-squared: 0.05232, Adjusted R-squared: -0.01841
## F-statistic: 0.7397 on 5 and 67 DF, p-value: 0.5964#anova(lm(RelativeFitness~PC1*TRT*sim+PC2*TRT*sim+PC3*TRT*sim+PC4*TRT*sim,RootFitAlpha))
summary(lm(RelativeFitness~PC1+PC2+PC3+PC4+InvSimp,RootFitAlpha%>%filter(TRT=="Alone")))##
## Call:
## lm(formula = RelativeFitness ~ PC1 + PC2 + PC3 + PC4 + InvSimp,
## data = RootFitAlpha %>% filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.66299 -0.33841 -0.02993 0.17095 1.09615
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.898837 0.643575 1.397 0.180
## PC1 0.113985 0.096335 1.183 0.252
## PC2 -0.075642 0.096894 -0.781 0.445
## PC3 -0.099766 0.211519 -0.472 0.643
## PC4 0.286787 0.177067 1.620 0.123
## InvSimp 0.007066 0.015514 0.455 0.654
##
## Residual standard error: 0.4939 on 18 degrees of freedom
## Multiple R-squared: 0.1975, Adjusted R-squared: -0.02539
## F-statistic: 0.8861 on 5 and 18 DF, p-value: 0.5105##
## Call:
## lm(formula = RelativeFitness ~ PC1 + PC2 + PC3 + PC4 + InvSimp,
## data = RootFitAlpha %>% filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.45015 -0.29744 -0.03431 0.24845 1.17892
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.770708 0.169949 4.535 2.45e-05 ***
## PC1 -0.108078 0.073328 -1.474 0.145
## PC2 -0.098238 0.106567 -0.922 0.360
## PC3 -0.142380 0.155322 -0.917 0.363
## PC4 0.110665 0.149888 0.738 0.463
## InvSimp 0.006901 0.004303 1.604 0.114
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3625 on 67 degrees of freedom
## Multiple R-squared: 0.0708, Adjusted R-squared: 0.001452
## F-statistic: 1.021 on 5 and 67 DF, p-value: 0.4125#anova(lm(RelativeFitness~PC1*TRT*InvSimp+PC2*TRT*InvSimp+PC3*TRT*InvSimp+PC4*TRT*InvSimp,RootFitAlpha))
summary(lm(RelativeFitness~PC1+PC2+PC3+PC4+even,RootFitAlpha%>%filter(TRT=="Alone")))##
## Call:
## lm(formula = RelativeFitness ~ PC1 + PC2 + PC3 + PC4 + even,
## data = RootFitAlpha %>% filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.69203 -0.38616 0.01376 0.14850 1.01700
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.52036 2.30274 1.529 0.144
## PC1 0.11189 0.09324 1.200 0.246
## PC2 -0.06868 0.08866 -0.775 0.449
## PC3 -0.05379 0.20776 -0.259 0.799
## PC4 0.26152 0.17450 1.499 0.151
## even -233.27167 228.46435 -1.021 0.321
##
## Residual standard error: 0.483 on 18 degrees of freedom
## Multiple R-squared: 0.2327, Adjusted R-squared: 0.01957
## F-statistic: 1.092 on 5 and 18 DF, p-value: 0.3985##
## Call:
## lm(formula = RelativeFitness ~ PC1 + PC2 + PC3 + PC4 + even,
## data = RootFitAlpha %>% filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.58133 -0.26839 -0.04516 0.20660 1.13952
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.17372 0.97368 3.259 0.00176 **
## PC1 -0.09717 0.07170 -1.355 0.17990
## PC2 -0.09793 0.10476 -0.935 0.35324
## PC3 -0.11787 0.15115 -0.780 0.43825
## PC4 0.07455 0.14849 0.502 0.61729
## even -206.75789 93.79970 -2.204 0.03095 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3567 on 67 degrees of freedom
## Multiple R-squared: 0.1004, Adjusted R-squared: 0.03324
## F-statistic: 1.495 on 5 and 67 DF, p-value: 0.2032##
## Call:
## lm(formula = RelativeFitness ~ PC1 + PC2 + PC3 + PC4 + rich,
## data = RootFitAlpha %>% filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.65902 -0.36686 -0.00494 0.17090 1.02814
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.202579 1.592825 -0.127 0.900
## PC1 0.108889 0.094578 1.151 0.265
## PC2 -0.076182 0.090884 -0.838 0.413
## PC3 -0.065021 0.208245 -0.312 0.758
## PC4 0.266736 0.175514 1.520 0.146
## rich 0.002936 0.003363 0.873 0.394
##
## Residual standard error: 0.4866 on 18 degrees of freedom
## Multiple R-squared: 0.2213, Adjusted R-squared: 0.004934
## F-statistic: 1.023 on 5 and 18 DF, p-value: 0.4335##
## Call:
## lm(formula = RelativeFitness ~ PC1 + PC2 + PC3 + PC4 + rich,
## data = RootFitAlpha %>% filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.55525 -0.28087 -0.03618 0.19842 1.11938
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.325487 0.609570 -0.534 0.595
## PC1 -0.114317 0.072162 -1.584 0.118
## PC2 -0.100462 0.104622 -0.960 0.340
## PC3 -0.142405 0.151864 -0.938 0.352
## PC4 0.074575 0.148336 0.503 0.617
## rich 0.003047 0.001365 2.232 0.029 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3564 on 67 degrees of freedom
## Multiple R-squared: 0.1019, Adjusted R-squared: 0.03489
## F-statistic: 1.521 on 5 and 67 DF, p-value: 0.1952# Interactions on fitness trait by alpha
EvenPC<-lm(RelativeFitness~TRT+Block+TRT:Block+TRT*PC1*EvenScaled+TRT*PC2*EvenScaled+TRT*PC3*EvenScaled+TRT*PC4*EvenScaled,RootFitAlpha)
anova(EvenPC)## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## TRT 1 0.1156 0.11565 1.5556 0.21641
## Block 3 8.0999 2.69998 36.3172 2.447e-14 ***
## PC1 1 0.0374 0.03735 0.5024 0.48075
## EvenScaled 1 0.0047 0.00465 0.0626 0.80317
## PC2 1 0.0024 0.00242 0.0325 0.85743
## PC3 1 0.2499 0.24990 3.3614 0.07093 .
## PC4 1 0.0031 0.00305 0.0410 0.84004
## TRT:Block 3 0.3390 0.11301 1.5201 0.21675
## TRT:PC1 1 0.0033 0.00332 0.0447 0.83317
## TRT:EvenScaled 1 0.1245 0.12451 1.6748 0.19981
## PC1:EvenScaled 1 0.0311 0.03105 0.4177 0.52017
## TRT:PC2 1 0.0016 0.00159 0.0214 0.88399
## EvenScaled:PC2 1 0.0066 0.00661 0.0889 0.76642
## TRT:PC3 1 0.0459 0.04588 0.6172 0.43472
## EvenScaled:PC3 1 0.1735 0.17346 2.3332 0.13108
## TRT:PC4 1 0.0008 0.00077 0.0104 0.91907
## EvenScaled:PC4 1 0.1506 0.15057 2.0253 0.15908
## TRT:PC1:EvenScaled 1 0.0279 0.02793 0.3757 0.54185
## TRT:EvenScaled:PC2 1 0.0085 0.00847 0.1139 0.73678
## TRT:EvenScaled:PC3 1 0.1939 0.19387 2.6077 0.11078
## TRT:EvenScaled:PC4 1 0.1652 0.16520 2.2221 0.14048
## Residuals 71 5.2784 0.07434
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1simPC<-lm(RelativeFitness~TRT+Block+TRT:Block+TRT*PC1*SimScaled+TRT*PC2*SimScaled+TRT*PC3*SimScaled+TRT*PC4*SimScaled,RootFitAlpha)
anova(simPC)## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## TRT 1 0.1156 0.11565 1.5114 0.222982
## Block 3 8.0999 2.69998 35.2858 4.504e-14 ***
## PC1 1 0.0374 0.03735 0.4882 0.487023
## SimScaled 1 0.0132 0.01318 0.1722 0.679412
## PC2 1 0.0021 0.00206 0.0269 0.870253
## PC3 1 0.2375 0.23753 3.1043 0.082392 .
## PC4 1 0.0022 0.00215 0.0281 0.867278
## TRT:Block 3 0.3188 0.10627 1.3888 0.253273
## TRT:PC1 1 0.0033 0.00331 0.0433 0.835723
## TRT:SimScaled 1 0.0332 0.03316 0.4334 0.512440
## PC1:SimScaled 1 0.0625 0.06248 0.8165 0.369266
## TRT:PC2 1 0.0006 0.00056 0.0073 0.932273
## SimScaled:PC2 1 0.0056 0.00564 0.0737 0.786853
## TRT:PC3 1 0.0967 0.09669 1.2636 0.264755
## SimScaled:PC3 1 0.0004 0.00039 0.0052 0.942968
## TRT:PC4 1 0.0006 0.00056 0.0074 0.931808
## SimScaled:PC4 1 0.0028 0.00278 0.0363 0.849475
## TRT:PC1:SimScaled 1 0.0000 0.00000 0.0000 0.994913
## TRT:SimScaled:PC2 1 0.0326 0.03261 0.4262 0.515983
## TRT:SimScaled:PC3 1 0.5603 0.56034 7.3230 0.008519 **
## TRT:SimScaled:PC4 1 0.0058 0.00577 0.0754 0.784453
## Residuals 71 5.4327 0.07652
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1richPC<-lm(RelativeFitness~TRT+Block+TRT:Block+TRT*PC1*richScaled+TRT*PC2*richScaled+TRT*PC3*richScaled+TRT*PC4*richScaled,RootFitAlpha)
anova(richPC)## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## TRT 1 0.1156 0.11565 1.6671 0.200840
## Block 3 8.0999 2.69998 38.9198 5.487e-15 ***
## PC1 1 0.0374 0.03735 0.5385 0.465490
## richScaled 1 0.0002 0.00018 0.0025 0.959872
## PC2 1 0.0022 0.00219 0.0315 0.859539
## PC3 1 0.2512 0.25119 3.6209 0.061114 .
## PC4 1 0.0028 0.00280 0.0404 0.841275
## TRT:Block 3 0.3265 0.10883 1.5687 0.204526
## TRT:PC1 1 0.0030 0.00297 0.0428 0.836618
## TRT:richScaled 1 0.1475 0.14750 2.1262 0.149209
## PC1:richScaled 1 0.0126 0.01256 0.1811 0.671744
## TRT:PC2 1 0.0041 0.00413 0.0596 0.807853
## richScaled:PC2 1 0.0000 0.00001 0.0001 0.992092
## TRT:PC3 1 0.0604 0.06045 0.8714 0.353741
## richScaled:PC3 1 0.1173 0.11733 1.6913 0.197638
## TRT:PC4 1 0.0036 0.00362 0.0522 0.819934
## richScaled:PC4 1 0.2167 0.21667 3.1233 0.081478 .
## TRT:PC1:richScaled 1 0.0987 0.09873 1.4232 0.236842
## TRT:richScaled:PC2 1 0.0047 0.00472 0.0681 0.794896
## TRT:richScaled:PC3 1 0.5596 0.55959 8.0663 0.005879 **
## TRT:richScaled:PC4 1 0.0741 0.07413 1.0686 0.304778
## Residuals 71 4.9255 0.06937
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1InSimPC<-lm(RelativeFitness~TRT+Block+TRT:Block+TRT*PC1*InvSimScaled+TRT*PC2*InvSimScaled+TRT*PC3*InvSimScaled+TRT*PC4*InvSimScaled,RootFitAlpha)
anova(InSimPC)## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## TRT 1 0.1156 0.11565 1.5247 0.220983
## Block 3 8.0999 2.69998 35.5956 3.746e-14 ***
## PC1 1 0.0374 0.03735 0.4925 0.485124
## InvSimScaled 1 0.0093 0.00930 0.1226 0.727252
## PC2 1 0.0023 0.00229 0.0302 0.862469
## PC3 1 0.2411 0.24110 3.1786 0.078884 .
## PC4 1 0.0023 0.00233 0.0307 0.861351
## TRT:Block 3 0.3180 0.10600 1.3974 0.250711
## TRT:PC1 1 0.0033 0.00329 0.0434 0.835652
## TRT:InvSimScaled 1 0.0466 0.04661 0.6145 0.435718
## PC1:InvSimScaled 1 0.0223 0.02233 0.2944 0.589144
## TRT:PC2 1 0.0002 0.00019 0.0025 0.960458
## InvSimScaled:PC2 1 0.0125 0.01245 0.1642 0.686582
## TRT:PC3 1 0.1008 0.10084 1.3295 0.252763
## InvSimScaled:PC3 1 0.0212 0.02123 0.2799 0.598445
## TRT:PC4 1 0.0022 0.00217 0.0286 0.866191
## InvSimScaled:PC4 1 0.0002 0.00018 0.0023 0.961627
## TRT:PC1:InvSimScaled 1 0.0036 0.00359 0.0473 0.828451
## TRT:InvSimScaled:PC2 1 0.0104 0.01041 0.1372 0.712137
## TRT:InvSimScaled:PC3 1 0.6097 0.60968 8.0379 0.005963 **
## TRT:InvSimScaled:PC4 1 0.0193 0.01931 0.2546 0.615389
## Residuals 71 5.3855 0.07585
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(lm(RelativeFitness~Block+PC1*InvSimScaled+PC2*InvSimScaled+PC3*InvSimScaled+PC4*InvSimScaled,RootFitAlpha%>%filter(TRT=="Alone")))##
## Call:
## lm(formula = RelativeFitness ~ Block + PC1 * InvSimScaled + PC2 *
## InvSimScaled + PC3 * InvSimScaled + PC4 * InvSimScaled, data = RootFitAlpha %>%
## filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.73064 -0.13685 -0.01639 0.07604 0.94018
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.492978 0.400872 1.230 0.2444
## Block2 -0.007347 0.344926 -0.021 0.9834
## Block3 0.863237 0.439762 1.963 0.0754 .
## Block4 0.697341 0.372942 1.870 0.0883 .
## PC1 -0.123130 0.138362 -0.890 0.3926
## InvSimScaled -0.337368 0.437350 -0.771 0.4567
## PC2 -0.036539 0.138113 -0.265 0.7962
## PC3 -0.336042 0.248689 -1.351 0.2038
## PC4 -0.154334 0.307107 -0.503 0.6252
## PC1:InvSimScaled 0.110013 0.195818 0.562 0.5855
## InvSimScaled:PC2 0.064561 0.195868 0.330 0.7479
## InvSimScaled:PC3 0.746208 0.582340 1.281 0.2264
## InvSimScaled:PC4 -0.077289 0.429471 -0.180 0.8605
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4986 on 11 degrees of freedom
## Multiple R-squared: 0.5003, Adjusted R-squared: -0.04489
## F-statistic: 0.9177 on 12 and 11 DF, p-value: 0.5601summary(lm(RelativeFitness~Block+PC1*InvSimScaled+PC2*InvSimScaled+PC3*InvSimScaled+PC4*InvSimScaled,RootFitAlpha%>%filter(TRT!="Alone")))##
## Call:
## lm(formula = RelativeFitness ~ Block + PC1 * InvSimScaled + PC2 *
## InvSimScaled + PC3 * InvSimScaled + PC4 * InvSimScaled, data = RootFitAlpha %>%
## filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.36529 -0.11695 -0.00889 0.06757 0.65663
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.6755687 0.0601181 11.237 < 2e-16 ***
## Block2 0.0968576 0.0739515 1.310 0.195
## Block3 0.7870096 0.0768932 10.235 8.80e-15 ***
## Block4 0.3397215 0.0757624 4.484 3.36e-05 ***
## PC1 0.0111949 0.0453835 0.247 0.806
## InvSimScaled -0.0009261 0.0325830 -0.028 0.977
## PC2 -0.0131862 0.0641224 -0.206 0.838
## PC3 -0.0545295 0.0979270 -0.557 0.580
## PC4 -0.0273720 0.0932287 -0.294 0.770
## PC1:InvSimScaled -0.0510828 0.0400841 -1.274 0.207
## InvSimScaled:PC2 -0.0590744 0.0668230 -0.884 0.380
## InvSimScaled:PC3 -0.0590930 0.0899463 -0.657 0.514
## InvSimScaled:PC4 0.0578580 0.0948641 0.610 0.544
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2102 on 60 degrees of freedom
## Multiple R-squared: 0.7203, Adjusted R-squared: 0.6643
## F-statistic: 12.87 on 12 and 60 DF, p-value: 1.696e-12summary(lm(RelativeFitness~Block+PC1*richScaled+PC2*richScaled+PC3*richScaled+PC4*richScaled,RootFitAlpha%>%filter(TRT=="Alone")))##
## Call:
## lm(formula = RelativeFitness ~ Block + PC1 * richScaled + PC2 *
## richScaled + PC3 * richScaled + PC4 * richScaled, data = RootFitAlpha %>%
## filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.88722 -0.12583 0.00799 0.06562 0.69200
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.610901 0.403832 1.513 0.1585
## Block2 0.076867 0.338040 0.227 0.8243
## Block3 0.631606 0.406460 1.554 0.1485
## Block4 0.885831 0.362321 2.445 0.0325 *
## PC1 -0.165221 0.128337 -1.287 0.2244
## richScaled 0.071313 0.235943 0.302 0.7681
## PC2 -0.008097 0.122535 -0.066 0.9485
## PC3 -0.612154 0.325889 -1.878 0.0871 .
## PC4 -0.244002 0.303774 -0.803 0.4389
## PC1:richScaled 0.213433 0.124198 1.718 0.1137
## richScaled:PC2 -0.048626 0.193401 -0.251 0.8061
## richScaled:PC3 0.544370 0.304099 1.790 0.1010
## richScaled:PC4 0.212981 0.361252 0.590 0.5674
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4524 on 11 degrees of freedom
## Multiple R-squared: 0.5886, Adjusted R-squared: 0.1398
## F-statistic: 1.311 on 12 and 11 DF, p-value: 0.3303summary(lm(RelativeFitness~Block+PC1*richScaled+PC2*richScaled+PC3*richScaled+PC4*richScaled,RootFitAlpha%>%filter(TRT!="Alone")))##
## Call:
## lm(formula = RelativeFitness ~ Block + PC1 * richScaled + PC2 *
## richScaled + PC3 * richScaled + PC4 * richScaled, data = RootFitAlpha %>%
## filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.37866 -0.10560 -0.00834 0.07669 0.61287
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.692264 0.060744 11.396 < 2e-16 ***
## Block2 0.081721 0.074871 1.091 0.279
## Block3 0.778519 0.077741 10.014 2.02e-14 ***
## Block4 0.339075 0.076532 4.431 4.06e-05 ***
## PC1 -0.002917 0.048868 -0.060 0.953
## richScaled -0.009322 0.036981 -0.252 0.802
## PC2 -0.014292 0.064311 -0.222 0.825
## PC3 -0.088420 0.096568 -0.916 0.364
## PC4 -0.040077 0.091576 -0.438 0.663
## PC1:richScaled -0.037381 0.045352 -0.824 0.413
## richScaled:PC2 -0.047871 0.067843 -0.706 0.483
## richScaled:PC3 -0.077137 0.089918 -0.858 0.394
## richScaled:PC4 -0.042623 0.104220 -0.409 0.684
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2111 on 60 degrees of freedom
## Multiple R-squared: 0.7178, Adjusted R-squared: 0.6614
## F-statistic: 12.72 on 12 and 60 DF, p-value: 2.169e-12summary(lm(RelativeFitness~Block+PC1*richScaled+PC2*richScaled+PC3*richScaled+PC4*richScaled,RootFitAlpha%>%filter(TRT=="Alone")))##
## Call:
## lm(formula = RelativeFitness ~ Block + PC1 * richScaled + PC2 *
## richScaled + PC3 * richScaled + PC4 * richScaled, data = RootFitAlpha %>%
## filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.88722 -0.12583 0.00799 0.06562 0.69200
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.610901 0.403832 1.513 0.1585
## Block2 0.076867 0.338040 0.227 0.8243
## Block3 0.631606 0.406460 1.554 0.1485
## Block4 0.885831 0.362321 2.445 0.0325 *
## PC1 -0.165221 0.128337 -1.287 0.2244
## richScaled 0.071313 0.235943 0.302 0.7681
## PC2 -0.008097 0.122535 -0.066 0.9485
## PC3 -0.612154 0.325889 -1.878 0.0871 .
## PC4 -0.244002 0.303774 -0.803 0.4389
## PC1:richScaled 0.213433 0.124198 1.718 0.1137
## richScaled:PC2 -0.048626 0.193401 -0.251 0.8061
## richScaled:PC3 0.544370 0.304099 1.790 0.1010
## richScaled:PC4 0.212981 0.361252 0.590 0.5674
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4524 on 11 degrees of freedom
## Multiple R-squared: 0.5886, Adjusted R-squared: 0.1398
## F-statistic: 1.311 on 12 and 11 DF, p-value: 0.3303summary(lm(RelativeFitness~Block+PC1*richScaled+PC2*richScaled+PC3*richScaled+PC4*richScaled,RootFitAlpha%>%filter(TRT!="Alone")))##
## Call:
## lm(formula = RelativeFitness ~ Block + PC1 * richScaled + PC2 *
## richScaled + PC3 * richScaled + PC4 * richScaled, data = RootFitAlpha %>%
## filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.37866 -0.10560 -0.00834 0.07669 0.61287
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.692264 0.060744 11.396 < 2e-16 ***
## Block2 0.081721 0.074871 1.091 0.279
## Block3 0.778519 0.077741 10.014 2.02e-14 ***
## Block4 0.339075 0.076532 4.431 4.06e-05 ***
## PC1 -0.002917 0.048868 -0.060 0.953
## richScaled -0.009322 0.036981 -0.252 0.802
## PC2 -0.014292 0.064311 -0.222 0.825
## PC3 -0.088420 0.096568 -0.916 0.364
## PC4 -0.040077 0.091576 -0.438 0.663
## PC1:richScaled -0.037381 0.045352 -0.824 0.413
## richScaled:PC2 -0.047871 0.067843 -0.706 0.483
## richScaled:PC3 -0.077137 0.089918 -0.858 0.394
## richScaled:PC4 -0.042623 0.104220 -0.409 0.684
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2111 on 60 degrees of freedom
## Multiple R-squared: 0.7178, Adjusted R-squared: 0.6614
## F-statistic: 12.72 on 12 and 60 DF, p-value: 2.169e-12Plotting 3D Plane
library(scatterplot3d) # This library will allow us to draw 3d plot
library("plot3D")
#Subset by treatment
RootFitAlphaAlone=RootFitAlpha%>%filter(TRT=="Alone")
RootFitAlphaComp=RootFitAlpha%>%filter(TRT!="Alone")
# Input data
x <- RootFitAlphaAlone$PC3
y <- RootFitAlphaAlone$sim
z <- RootFitAlphaAlone$RelativeFitness
# Compute the linear regression (z = ax + by + d)
fit <- lm(z ~ x + y)
# predict values on regular xy grid
grid.lines = 26
x.pred <- seq(min(x), max(x), length.out = grid.lines)
y.pred <- seq(min(y), max(y), length.out = grid.lines)
xy <- expand.grid( x = x.pred, y = y.pred)
z.pred <- matrix(predict(fit, newdata = xy),
nrow = grid.lines, ncol = grid.lines)
# fitted points for droplines to surface
fitpoints <- predict(fit)
# Root trait × Treatment × Simpson diversity
# scatter plot with regression plane
scatter3D(x, y, z, pch = 18, cex = 2,
theta =135, phi = 10, colvar = NULL, col = "blue",
xlab = "Root Size", ylab = "Simpson Diversity", zlab = "Relative Fitness",
surf = list(x = x.pred, y = y.pred, z = z.pred,
facets = NA, fit = fitpoints), main = "Absence of Competition")
# Repeat for competition treatment
# Input data
x <- RootFitAlphaComp$PC3
y <- RootFitAlphaComp$sim
z <- RootFitAlphaComp$RelativeFitness
# Compute the linear regression (z = ax + by + d)
fit <- lm(z ~ x + y)
# predict values on regular xy grid
grid.lines = 26
x.pred <- seq(min(x), max(x), length.out = grid.lines)
y.pred <- seq(min(y), max(y), length.out = grid.lines)
xy <- expand.grid( x = x.pred, y = y.pred)
z.pred <- matrix(predict(fit, newdata = xy),
nrow = grid.lines, ncol = grid.lines)
# fitted points for droplines to surface
fitpoints <- predict(fit)
# scatter plot with regression plane
s3d <- scatterplot3d(x,y,z, highlight.3d=FALSE, scale.y=.5, pch=16, main = "Presence of Competition",
xlab = "Root Size", ylab = "Simpson Diversity", zlab = "Relative Fitness", color="steelblue",angle=30) # Now adding some points to the "scatterplot3d"
s3d$points3d(seq(10,20,2), seq(85,60,-5), seq(60,10,-10),col="steelblue", type="h", pch=16,scale=2)# Now adding a regression plane to the "scatterplot3d"attach(trees)## Warning in segments(x, y, x, y2, ...): "scale" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "scale" is not a
## graphical parameter
scatter3D(x, y, z, pch = 18, cex = 2,
theta =45, phi = 10, colvar = NULL, col = "blue",
xlab = "Root Size", ylab = "Simpson Diversity", zlab = "Relative Fitness",
surf = list(x = x.pred, y = y.pred, z = z.pred,
facets = NA, fit = fitpoints), main = "Presence of Competition")
points3D(x, y, z, pch = 16, col="black", alpha = 0.8, add=TRUE)
# Root trait × Treatment × Inverse Simpson diversity
# Competition treatment
y <- RootFitAlphaComp$InvSimp
# Compute the linear regression (z = ax + by + d)
fit <- lm(z ~ x + y)
# predict values on regular xy grid
grid.lines = 26
x.pred <- seq(min(x), max(x), length.out = grid.lines)
y.pred <- seq(min(y), max(y), length.out = grid.lines)
xy <- expand.grid( x = x.pred, y = y.pred)
z.pred <- matrix(predict(fit, newdata = xy),
nrow = grid.lines, ncol = grid.lines)
scatter3D(x, y, z, pch = 18, cex = 2,
theta =45, phi = 10, colvar = NULL, col = "blue",
xlab = "Root Size", ylab = "Inverse Simpson Diversity", zlab = "Relative Fitness",
surf = list(x = x.pred, y = y.pred, z = z.pred,
facets = NA, fit = fitpoints), main = "Presence of Competition")
points3D(x, y, z, pch = 16, col="black", alpha = 0.8, add=TRUE)
# Absence of competition treatment
y <- RootFitAlphaAlone$InvSimp
x<-RootFitAlphaAlone$PC3
z<-RootFitAlphaAlone$RelativeFitness
# Compute the linear regression (z = ax + by + d)
fit <- lm(z ~ x + y)
# fitted points for droplines to surface
fitpoints <- predict(fit)
# predict values on regular xy grid
grid.lines = 26
x.pred <- seq(min(x), max(x), length.out = grid.lines)
y.pred <- seq(min(y), max(y), length.out = grid.lines)
xy <- expand.grid( x = x.pred, y = y.pred)
z.pred <- matrix(predict(fit, newdata = xy),
nrow = grid.lines, ncol = grid.lines)
scatter3D(x, y, z, pch = 18, cex = 2,
theta =45, phi = 10, colvar = NULL, col = "blue",
xlab = "Root Size", ylab = "Inverse Simpson Diversity", zlab = "Relative Fitness",
surf = list(x = x.pred, y = y.pred, z = z.pred,
facets = NA, fit = fitpoints), main = "Absence of Competition")
# Root trait × Treatment × Richness
# Competition treatment
y <- RootFitAlphaComp$rich
x<-RootFitAlphaComp$PC3
z<-RootFitAlphaComp$RelativeFitness
# Compute the linear regression (z = ax + by + d)
fit <- lm(z ~ x + y)
fitpoints <- predict(fit)
# predict values on regular xy grid
grid.lines = 26
x.pred <- seq(min(x), max(x), length.out = grid.lines)
y.pred <- seq(min(y), max(y), length.out = grid.lines)
xy <- expand.grid( x = x.pred, y = y.pred)
z.pred <- matrix(predict(fit, newdata = xy),
nrow = grid.lines, ncol = grid.lines)
scatter3D(x, y, z, pch = 18, cex = 2,
theta =45, phi = 10, colvar = NULL, col = "blue",
xlab = "Root Size", ylab = "Richness", zlab = "Relative Fitness",
surf = list(x = x.pred, y = y.pred, z = z.pred,
facets = NA, fit = fitpoints), main = "Presence of Competition")
# Absence of competition treatment
y <- RootFitAlphaAlone$rich
x<-RootFitAlphaAlone$PC3
z<-RootFitAlphaAlone$RelativeFitness
# Compute the linear regression (z = ax + by + d)
fit <- lm(z ~ x + y)
# fitted points for droplines to surface
fitpoints <- predict(fit)
# predict values on regular xy grid
grid.lines = 26
x.pred <- seq(min(x), max(x), length.out = grid.lines)
y.pred <- seq(min(y), max(y), length.out = grid.lines)
xy <- expand.grid( x = x.pred, y = y.pred)
z.pred <- matrix(predict(fit, newdata = xy),
nrow = grid.lines, ncol = grid.lines)
scatter3D(x, y, z, pch = 18, cex = 2,
theta =45, phi = 10, colvar = NULL, col = "blue",
xlab = "Root Size", ylab = "Richness", zlab = "Relative Fitness",
surf = list(x = x.pred, y = y.pred, z = z.pred,
facets = NA, fit = fitpoints), main = "Absence of Competition")
Quadratic relationships w fitness
RootFitAlpha$rich2<-RootFitAlpha$rich*RootFitAlpha$rich
RootFitAlpha$sim2<-RootFitAlpha$sim*RootFitAlpha$sim
RootFitAlpha$InvSimp2<-RootFitAlpha$InvSimp*RootFitAlpha$InvSimp
RootFitAlpha$even2<-RootFitAlpha$even*RootFitAlpha$even
AncovRich<-lm(RelativeFitness~rich2+rich+rich2*Block*Trt,RootFitAlpha)
AncovSim<-lm(RelativeFitness~sim2+sim+sim2*Block*Trt,RootFitAlpha)
AncovInSim<-lm(RelativeFitness~InvSimp2+InvSimp+InvSimp2*Block*Trt,RootFitAlpha)
AncovEven<-lm(RelativeFitness~even2+even+even2*Block*Trt,RootFitAlpha)
anova(AncovRich) # Significant quadratic richness term## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## rich2 1 0.8339 0.83392 10.8189 0.001495 **
## rich 1 0.0112 0.01123 0.1457 0.703738
## Block 3 7.3905 2.46349 31.9602 1.109e-13 ***
## Trt 1 0.0445 0.04450 0.5773 0.449603
## rich2:Block 3 0.1592 0.05307 0.6885 0.561677
## rich2:Trt 1 0.0050 0.00496 0.0644 0.800335
## Block:Trt 3 0.4176 0.13920 1.8059 0.152765
## rich2:Block:Trt 3 0.0354 0.01180 0.1531 0.927421
## Residuals 80 6.1664 0.07708
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## sim2 1 0.1365 0.13653 1.7802 0.1859
## sim 1 0.1116 0.11159 1.4550 0.2313
## Block 3 7.9356 2.64520 34.4904 2.08e-14 ***
## Trt 1 0.0555 0.05551 0.7238 0.3974
## sim2:Block 3 0.0577 0.01925 0.2510 0.8604
## sim2:Trt 1 0.0001 0.00012 0.0016 0.9682
## Block:Trt 3 0.3760 0.12533 1.6341 0.1880
## sim2:Block:Trt 3 0.2551 0.08504 1.1088 0.3505
## Residuals 80 6.1355 0.07669
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## InvSimp2 1 0.5022 0.50221 6.4441 0.01307 *
## InvSimp 1 0.3673 0.36727 4.7127 0.03291 *
## Block 3 7.3351 2.44502 31.3733 1.652e-13 ***
## Trt 1 0.0390 0.03902 0.5007 0.48127
## InvSimp2:Block 3 0.0231 0.00769 0.0987 0.96050
## InvSimp2:Trt 1 0.0003 0.00028 0.0036 0.95217
## Block:Trt 3 0.3859 0.12863 1.6505 0.18435
## InvSimp2:Block:Trt 3 0.1762 0.05873 0.7537 0.52344
## Residuals 80 6.2347 0.07793
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## even2 1 0.9754 0.97536 13.2264 0.0004869 ***
## even 1 0.0227 0.02273 0.3083 0.5802959
## Block 3 7.3830 2.46100 33.3724 4.321e-14 ***
## Trt 1 0.0418 0.04178 0.5666 0.4538191
## even2:Block 3 0.1926 0.06420 0.8706 0.4599352
## even2:Trt 1 0.0180 0.01796 0.2435 0.6230372
## Block:Trt 3 0.4254 0.14179 1.9227 0.1325461
## even2:Block:Trt 3 0.1054 0.03513 0.4764 0.6996033
## Residuals 80 5.8995 0.07374
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Quadratic w Root Size
# Include root size and interactions as covariates
AncovRich<-lm(RelativeFitness~rich2+rich+rich2*Block*Trt*PC3-rich2:Block:TRT:PC3,RootFitAlpha)
AncovSim<-lm(RelativeFitness~sim2+sim+sim2*Block*Trt*PC3-sim2:Block:TRT:PC3,RootFitAlpha)
AncovInSim<-lm(RelativeFitness~InvSimp2+InvSimp+InvSimp2*Block*Trt*PC3-InvSimp2:Block:TRT:PC3,RootFitAlpha)
AncovEven<-lm(RelativeFitness~even2+even+even2*Block*Trt*PC3-even2:Block:TRT:PC3,RootFitAlpha)
anova(AncovRich) # Significant quadratic richness term, NS treatment interaction## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## rich2 1 0.8339 0.83392 13.3655 0.0005193 ***
## rich 1 0.0112 0.01123 0.1799 0.6728502
## Block 3 7.3905 2.46349 39.4833 1.449e-14 ***
## Trt 1 0.0445 0.04450 0.7132 0.4015301
## PC3 1 0.2519 0.25187 4.0368 0.0487390 *
## rich2:Block 3 0.1126 0.03754 0.6016 0.6163056
## rich2:Trt 1 0.0003 0.00032 0.0051 0.9430860
## Block:Trt 3 0.3684 0.12280 1.9681 0.1276376
## rich2:PC3 1 0.0264 0.02635 0.4224 0.5180901
## Block:PC3 3 0.4803 0.16009 2.5659 0.0622405 .
## Trt:PC3 1 0.2189 0.21890 3.5084 0.0656256 .
## rich2:Block:Trt 3 0.0343 0.01142 0.1830 0.9075514
## rich2:Block:PC3 3 0.7860 0.26201 4.1994 0.0089364 **
## rich2:Trt:PC3 1 0.0565 0.05646 0.9049 0.3450557
## Block:Trt:PC3 3 0.3819 0.12730 2.0403 0.1170493
## rich2:Block:Trt:PC3 3 0.0730 0.02433 0.3900 0.7605724
## Residuals 64 3.9932 0.06239
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## sim2 1 0.1365 0.13653 2.0807 0.15405
## sim 1 0.1116 0.11159 1.7006 0.19689
## Block 3 7.9356 2.64520 40.3114 9.429e-15 ***
## Trt 1 0.0555 0.05551 0.8459 0.36116
## PC3 1 0.2032 0.20321 3.0969 0.08322 .
## sim2:Block 3 0.0342 0.01139 0.1736 0.91385
## sim2:Trt 1 0.0010 0.00095 0.0145 0.90456
## Block:Trt 3 0.3653 0.12176 1.8556 0.14606
## sim2:PC3 1 0.0171 0.01708 0.2603 0.61164
## Block:PC3 3 0.4708 0.15693 2.3916 0.07675 .
## Trt:PC3 1 0.1537 0.15368 2.3420 0.13086
## sim2:Block:Trt 3 0.2445 0.08150 1.2420 0.30186
## sim2:Block:PC3 3 0.0260 0.00868 0.1322 0.94054
## sim2:Trt:PC3 1 0.3747 0.37465 5.7095 0.01983 *
## Block:Trt:PC3 3 0.6030 0.20102 3.0634 0.03427 *
## sim2:Block:Trt:PC3 3 0.1314 0.04380 0.6676 0.57506
## Residuals 64 4.1996 0.06562
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(AncovInSim) # Significant quadratic Inverse Simpson term, significant trt by root by microbe **## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## InvSimp2 1 0.5022 0.50221 7.4716 0.008095 **
## InvSimp 1 0.3673 0.36727 5.4641 0.022551 *
## Block 3 7.3351 2.44502 36.3756 7.652e-14 ***
## Trt 1 0.0390 0.03902 0.5805 0.448923
## PC3 1 0.2320 0.23202 3.4518 0.067783 .
## InvSimp2:Block 3 0.0105 0.00349 0.0520 0.984223
## InvSimp2:Trt 1 0.0001 0.00008 0.0012 0.972053
## Block:Trt 3 0.3621 0.12071 1.7958 0.156878
## InvSimp2:PC3 1 0.0259 0.02593 0.3858 0.536715
## Block:PC3 3 0.4879 0.16264 2.4197 0.074199 .
## Trt:PC3 1 0.1329 0.13292 1.9776 0.164483
## InvSimp2:Block:Trt 3 0.1780 0.05933 0.8826 0.454934
## InvSimp2:Block:PC3 3 0.0087 0.00291 0.0434 0.987881
## InvSimp2:Trt:PC3 1 0.3694 0.36945 5.4964 0.022171 *
## Block:Trt:PC3 3 0.5965 0.19884 2.9582 0.038870 *
## InvSimp2:Block:Trt:PC3 3 0.1141 0.03805 0.5661 0.639378
## Residuals 64 4.3018 0.06722
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Analysis of Variance Table
##
## Response: RelativeFitness
## Df Sum Sq Mean Sq F value Pr(>F)
## even2 1 0.9754 0.97536 16.2336 0.0001512 ***
## even 1 0.0227 0.02273 0.3784 0.5406669
## Block 3 7.3830 2.46100 40.9601 6.763e-15 ***
## Trt 1 0.0418 0.04178 0.6954 0.4074239
## PC3 1 0.3382 0.33817 5.6284 0.0206883 *
## even2:Block 3 0.1914 0.06380 1.0618 0.3716135
## even2:Trt 1 0.0061 0.00614 0.1022 0.7502042
## Block:Trt 3 0.3612 0.12042 2.0041 0.1222425
## even2:PC3 1 0.0144 0.01444 0.2403 0.6256392
## Block:PC3 3 0.3936 0.13119 2.1834 0.0985645 .
## Trt:PC3 1 0.1842 0.18418 3.0654 0.0847648 .
## even2:Block:Trt 3 0.0191 0.00637 0.1060 0.9562937
## even2:Block:PC3 3 0.6193 0.20642 3.4357 0.0219896 *
## even2:Trt:PC3 1 0.0703 0.07028 1.1697 0.2835151
## Block:Trt:PC3 3 0.5243 0.17477 2.9087 0.0412432 *
## even2:Block:Trt:PC3 3 0.0734 0.02447 0.4072 0.7483085
## Residuals 64 3.8453 0.06008
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Within treatment for inverse simpson and simpson diversity
Sim_Size_Alone<-lm(RelativeFitness~InvSimp2+PC3,RootFitAlpha %>% filter(TRT=="Alone"))
summary(Sim_Size_Alone)##
## Call:
## lm(formula = RelativeFitness ~ InvSimp2 + PC3, data = RootFitAlpha %>%
## filter(TRT == "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.4977 -0.3350 -0.2025 0.2437 1.3048
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.793e-01 3.207e-01 2.742 0.0122 *
## InvSimp2 9.942e-05 1.895e-04 0.525 0.6053
## PC3 -1.756e-01 2.005e-01 -0.875 0.3912
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4989 on 21 degrees of freedom
## Multiple R-squared: 0.04498, Adjusted R-squared: -0.04598
## F-statistic: 0.4945 on 2 and 21 DF, p-value: 0.6168Sim_Size_Comp<-lm(RelativeFitness~InvSimp2+PC3,RootFitAlpha %>% filter(TRT!="Alone"))
summary(Sim_Size_Comp)##
## Call:
## lm(formula = RelativeFitness ~ InvSimp2 + PC3, data = RootFitAlpha %>%
## filter(TRT != "Alone"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.50941 -0.32491 0.00258 0.23801 1.14760
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.492e-01 8.914e-02 9.527 2.88e-14 ***
## InvSimp2 9.495e-05 5.112e-05 1.857 0.0675 .
## PC3 -4.783e-02 1.195e-01 -0.400 0.6901
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3592 on 70 degrees of freedom
## Multiple R-squared: 0.04701, Adjusted R-squared: 0.01979
## F-statistic: 1.727 on 2 and 70 DF, p-value: 0.1854